Methods, systems, and devices for sensor fusion

ABSTRACT

A single, optimal, fused sensor glucose value may be calculated based on respective sensor glucose values of a plurality of redundant working electrodes (WEs) of a glucose sensor. Respective electrochemical impedance spectroscopy (EIS) procedures may be performed for each of the WEs to obtain values of membrane resistance (Rmem) for each WE. A noise value and a calibration factor (CF) value may be calculated for each WE, and respective fusion weights may be calculated for Rmem, noise, and CF for each WE. An overall fusion weight may then be calculated based on the WE&#39;s Rmem fusion weight, noise fusion weight, and CF fusion weight, such that a single, optimal, fused sensor glucose value may be calculated based on the respective overall fusion weight and sensor glucose value of each of the plurality of redundant working electrodes.

FIELD OF THE INVENTION

Embodiments of this invention are related generally to subcutaneous andimplantable sensor devices and, in particular embodiments, to methods,systems, and devices for providing a single, optimal, fused sensor valueto a user.

BACKGROUND OF THE INVENTION

Over the years, a variety of sensors have been developed for detectingand/or quantifying specific agents or compositions in a patient's blood,which enable patients and medical personnel to monitor physiologicalconditions within the patient's body. Illustratively, subjects may wishto monitor blood glucose levels in a subject's body on a continuingbasis. Thus, glucose sensors have been developed for use in obtaining anindication of blood glucose levels in a diabetic patient. Such readingsare useful in monitoring and/or adjusting a treatment regimen whichtypically includes the regular administration of insulin to the patient.

Presently, a patient can measure his/her blood glucose (BG) using a BGmeasurement device (i.e., glucose meter), such as a test strip meter, acontinuous glucose measurement system (or a continuous glucose monitor),or a hospital hemacue. BG measurement devices use various methods tomeasure the BG level of a patient, such as a sample of the patient'sblood, a sensor in contact with a bodily fluid, an optical sensor, anenzymatic sensor, or a fluorescent sensor. When the BG measurementdevice has generated a BG measurement, the measurement is displayed onthe BG measurement device.

Current continuous glucose measurement systems include subcutaneous (orshort-term) sensors and implantable (or long-term) sensors. Sensors havebeen applied in a telemetered characteristic monitor system. Asdescribed, e.g., in commonly-assigned U.S. Pat. No. 6,809,653, theentire contents of which are incorporated herein by reference, atelemetered system using an electrochemical sensor includes a remotelylocated data receiving device, a sensor for producing signals indicativeof a characteristic of a user, and a transmitter device for processingsignals received from the sensor and for wirelessly transmitting theprocessed signals to the remotely located data receiving device. Thedata receiving device may be a characteristic monitor, a data receiverthat provides data to another device, an RF programmer, a medicationdelivery device (such as an infusion pump), or the like.

Regardless of whether the data receiving device (e.g., a glucosemonitor), the transmitter device, and the sensor (e.g., a glucosesensor) communicate wirelessly or via an electrical wire connection, acharacteristic monitoring system of the type described above is ofpractical use only after it has been calibrated based on the uniquecharacteristics of the individual user. According to the current stateof the art, the user is required to externally calibrate the sensor.More specifically, and in connection with the illustrative example of adiabetic patient, the latter is required to utilize a finger-stick bloodglucose meter reading an average of two-four times per day for theduration that the characteristic monitor system is used. Each time,blood is drawn from the user's finger and analyzed by the blood glucosemeter to provide a real-time blood sugar level for the user. The userthen inputs this data into the glucose monitor as the user's currentblood sugar level which is used to calibrate the glucose monitoringsystem.

Such external calibrations, however, are disadvantageous for variousreasons. For example, blood glucose meters are not perfectly accurateand include inherent margins of error. Moreover, even if completelyaccurate, blood glucose meters are susceptible to improper use; forexample, if the user has handled candy or other sugar-containingsubstance immediately prior to performing the finger stick, with some ofthe sugar sticking to the user's fingers, the blood sugar analysis willresult in an inaccurate blood sugar level indication. Furthermore, thereis a cost, not to mention pain and discomfort, associated with eachapplication of the finger stick.

The current state of the art in continuous glucose monitoring (CGM) islargely adjunctive, meaning that the readings provided by a CGM device(including, e.g., an implantable or subcutaneous sensor) cannot be usedwithout a reference value in order to make a clinical decision. Thereference value, in turn, must be obtained from a finger stick using,e.g., a BG meter. The reference value is needed because there is alimited amount of information that is available from the sensor/sensingcomponent. Specifically, the only pieces of information that arecurrently provided by the sensing component for processing are the rawsensor value (i.e., the sensor current or Isig) and the counter voltage.Therefore, during analysis, if it appears that the raw sensor signal isabnormal (e.g., if the signal is decreasing), the only way one candistinguish between a sensor failure and a physiological change withinthe user/patient (i.e., glucose level changing in the body) is byacquiring a reference glucose value via a finger stick. As is known, thereference finger stick is also used for calibrating the sensor.

The art has searched for ways to eliminate or, at the very least,minimize, the number of finger sticks that are necessary for calibrationand for assessing sensor health. However, given the number and level ofcomplexity of the multitude of sensor failure modes, no satisfactorysolution has been found. At most, diagnostics have been developed thatare based on either direct assessment of the Isig, or on comparison ofmultiple Isigs, e.g., from redundant and/or orthogonally redundant,sensors and/or electrodes. In either case, because the Isig tracks thelevel of glucose in the body, by definition, it is not analyteindependent. As such, by itself, the Isig is not a reliable source ofinformation for sensor diagnostics, nor is it a reliable predictor forcontinued sensor performance.

Another limitation that has existed in the art thus far has been thelack of sensor electronics that can not only run the sensor, but alsoperform real-time sensor and electrode diagnostics, and do so forredundant electrodes, all while managing the sensor's power supply. Tobe sure, the concept of electrode redundancy has been around for quitesome time. However, up until now, there has been little to no success inusing electrode redundancy not only for obtaining more than one readingat a time, but also for assessing the relative health of the redundantelectrodes, the overall reliability of the sensor, and the frequency ofthe need, if at all, for calibration reference values while, at thesame, delivering a single, optimal glucose value to the user.

SUMMARY

According to an embodiment of the invention, a method of calculating asingle, fused sensor glucose value based on respective sensor glucosevalues of a plurality of redundant working electrodes of a glucosesensor comprises performing respective electrochemical impedancespectroscopy (EIS) procedures for each of the plurality of redundantworking electrodes to obtain values of membrane resistance (Rmem) foreach said working electrode; calculating a respective Rmem fusion weightfor each said working electrode based on the respective Rmem value foreach of the plurality of working electrodes; measuring a noise value foreach of the plurality of working electrodes; calculating a respectivenoise fusion weight for each said working electrode based on therespective noise value for each of the plurality of working electrodes;measuring a calibration factor (CF) value for each of the plurality ofworking electrodes; calculating a respective CF fusion weight for eachsaid working electrode based on the respective CF value for each of theplurality of working electrodes; for each of the plurality ofelectrodes, calculating an overall fusion weight based on saidelectrode's Rmem fusion weight, noise fusion weight, and CF fusionweight; and calculating said single, fused sensor glucose value based onthe respective overall fusion weight and sensor glucose value of each ofthe plurality of redundant working electrodes.

In accordance with another embodiment of the invention, a program codestorage device comprises a computer-readable medium andcomputer-readable program code, stored on the computer-readable medium,the computer-readable program code having instructions which, whenexecuted, cause a physical microcontroller to perform a method ofcalculating a single, fused sensor glucose value based on respectivesensor glucose values of a plurality of redundant working electrodes ofa glucose sensor by: performing respective electrochemical impedancespectroscopy (EIS) procedures for each of the plurality of redundantworking electrodes to obtain values of membrane resistance (Rmem) foreach said working electrode; calculating a respective Rmem fusion weightfor each said working electrode based on the respective Rmem value foreach of the plurality of working electrodes; obtaining a noise value foreach of the plurality of working electrodes; calculating a respectivenoise fusion weight for each said working electrode based on therespective noise value for each of the plurality of working electrodes;obtaining a calibration factor (CF) value for each of the plurality ofworking electrodes; calculating a respective CF fusion weight for eachsaid working electrode based on the respective CF value for each of theplurality of working electrodes; for each of the plurality ofelectrodes, calculating an overall fusion weight based on saidelectrode's Rmem fusion weight, noise fusion weight, and CF fusionweight; and calculating said single, fused sensor glucose value based onthe respective overall fusion weight and sensor glucose value of each ofthe plurality of redundant working electrodes.

BRIEF DESCRIPTION OF THE DRAWINGS

A detailed description of embodiments of the invention will be made withreference to the accompanying drawings, wherein like numerals designatecorresponding parts in the figures.

FIG. 1 is a perspective view of a subcutaneous sensor insertion set andblock diagram of a sensor electronics device according to an embodimentof the invention.

FIG. 2A illustrates a substrate having two sides, a first side whichcontains an electrode configuration and a second side which containselectronic circuitry.

FIG. 2B illustrates a general block diagram of an electronic circuit forsensing an output of a sensor.

FIG. 3 illustrates a block diagram of a sensor electronics device and asensor including a plurality of electrodes according to an embodiment ofthe invention.

FIG. 4 illustrates an alternative embodiment of the invention includinga sensor and a sensor electronics device according to an embodiment ofthe invention.

FIG. 5 illustrates an electronic block diagram of the sensor electrodesand a voltage being applied to the sensor electrodes according to anembodiment of the invention.

FIG. 6A illustrates a method of applying pulses during a stabilizationtimeframe in order to reduce the stabilization timeframe according to anembodiment of the invention.

FIG. 6B illustrates a method of stabilizing sensors according to anembodiment of the invention.

FIG. 6C illustrates utilization of feedback in stabilizing the sensorsaccording to an embodiment of the invention.

FIG. 7 illustrates an effect of stabilizing a sensor according to anembodiment of the invention.

FIG. 8A illustrates a block diagram of a sensor electronics device and asensor including a voltage generation device according to an embodimentof the invention.

FIG. 8B illustrates a voltage generation device to implement thisembodiment of the invention.

FIG. 8C illustrates a voltage generation device to generate two voltagevalues according to an embodiment of the invention.

FIG. 8D illustrates a voltage generation device having three voltagegeneration systems, according to embodiments of the invention.

FIG. 9A illustrates a sensor electronics device including amicrocontroller for generating voltage pulses according to an embodimentof the invention.

FIG. 9B illustrates a sensor electronics device including an analyzationmodule according to an embodiment of the invention.

FIG. 10 illustrates a block diagram of a sensor system includinghydration electronics according to an embodiment of the invention.

FIG. 11 illustrates an embodiment of the invention including amechanical switch to assist in determining a hydration time.

FIG. 12 illustrates a method of detection of hydration according to anembodiment of the invention.

FIG. 13A illustrates a method of hydrating a sensor according to anembodiment of the present invention.

FIG. 13B illustrates an additional method for verifying hydration of asensor according to an embodiment of the invention.

FIGS. 14A, 14B, and 14C illustrate methods of combining hydrating of asensor with stabilizing a sensor according to an embodiment of theinvention.

FIG. 15A illustrates EIS-based analysis of system response to theapplication of a periodic AC signal in accordance with embodiments ofthe invention.

FIG. 15B illustrates a known circuit model for electrochemical impedancespectroscopy.

FIG. 16A illustrates an example of a Nyquist plot where, for a selectedfrequency spectrum from 0.1 Hz to 1000 Mhz, AC voltages plus a DCvoltage (DC bias) are applied to the working electrode in accordancewith embodiments of the invention.

FIG. 16B shows another example of a Nyquist plot with a linear fit forthe relatively-lower frequencies and the intercept approximating thevalue of real impedance at the relatively-higher frequencies.

FIGS. 16C and 16D show, respectively, infinite and finite glucose sensorresponse to a sinusoidal working potential.

FIG. 16E shows a Bode plot for magnitude in accordance with embodimentsof the invention.

FIG. 16F shows a Bode plot for phase in accordance with embodiments ofthe invention.

FIG. 17 illustrates the changing Nyquist plot of sensor impedance as thesensor ages in accordance with embodiments of the invention.

FIG. 18 illustrates methods of applying EIS technique in stabilizing anddetecting the age of the sensor in accordance with embodiments of theinvention.

FIG. 19 illustrates a schedule for performing the EIS procedure inaccordance with embodiments of the invention.

FIG. 20 illustrates a method of detecting and repairing a sensor usingEIS procedures in conjunction with remedial action in accordance withembodiments of the invention.

FIGS. 21A and 21B illustrate examples of a sensor remedial action inaccordance with embodiments of the invention.

FIG. 22 shows a Nyquist plot for a normally-functioning sensor where theNyquist slope gradually increases, and the intercept graduallydecreases, as the sensor wear-time progresses.

FIG. 23A shows raw current signal (Isig) from two redundant workingelectrodes, and the electrodes' respective real impedances at 1 kHz, inaccordance with embodiments of the invention.

FIG. 23B shows the Nyquist plot for the first working electrode (WE1) ofFIG. 23A.

FIG. 23C shows the Nyquist plot for the second working electrode (WE2)of FIG. 23A.

FIG. 24 illustrates examples of signal dip for two redundant workingelectrodes, and the electrodes' respective real impedances at 1 kHz, inaccordance with embodiments of the invention.

FIG. 25A illustrates substantial glucose independence of real impedance,imaginary impedance, and phase at relatively-higher frequencies for anormally-functioning glucose sensor in accordance with embodiments ofthe invention.

FIG. 25B shows illustrative examples of varying levels of glucosedependence of real impedance at the relatively-lower frequencies inaccordance with embodiments of the invention.

FIG. 25C shows illustrative examples of varying levels of glucosedependence of phase at the relatively-lower frequencies in accordancewith embodiments of the invention.

FIG. 26 shows the trending for 1 kHz real impedance, 1 kHz imaginaryimpedance, and relatively-higher frequency phase as a glucose sensorloses sensitivity as a result of oxygen deficiency at the sensorinsertion site, according to embodiments of the invention.

FIG. 27 shows Isig and phase for an in-vitro simulation of oxygendeficit at different glucose concentrations in accordance withembodiments of the invention.

FIGS. 28A-28C show an example of oxygen deficiency-led sensitivity losswith redundant working electrodes WE1 and WE2, as well as theelectrodes' EIS-based parameters, in accordance with embodiments of theinvention.

FIG. 28D shows EIS-induced spikes in the raw Isig for the example ofFIGS. 28A-28C.

FIG. 29 shows an example of sensitivity loss due to oxygen deficiencythat is caused by an occlusion, in accordance with embodiments of theinvention.

FIGS. 30A-30C show an example of sensitivity loss due to bio-fouling,with redundant working electrodes WE1 and WE2, as well as theelectrodes' EIS-based parameters, in accordance with embodiments of theinvention.

FIG. 30D shows EIS-induced spikes in the raw Isig for the example ofFIGS. 30A-30C.

FIG. 31 shows a diagnostic procedure for sensor fault detection inaccordance with embodiments of the invention.

FIGS. 32A and 32B show another diagnostic procedure for sensor faultdetection in accordance with embodiments of the invention.

FIG. 33A shows a top-level flowchart involving a current (Isig)-basedfusion algorithm in accordance with embodiments of the invention.

FIG. 33B shows a top-level flowchart involving a sensor glucose(SG)-based fusion algorithm in accordance with embodiments of theinvention.

FIG. 34 shows details of the sensor glucose (SG)-based fusion algorithmof FIG. 33B in accordance with embodiments of the invention.

FIG. 35 shows details of the current (Isig)-based fusion algorithm ofFIG. 33A in accordance with embodiments of the invention.

FIG. 36 is an illustration of calibration for a sensor in steady state,in accordance with embodiments of the invention.

FIG. 37 is an illustration of calibration for a sensor in transition, inaccordance with embodiments of the invention.

FIG. 38A is an illustration of EIS-based dynamic slope (with slopeadjustment) in accordance with embodiments of the invention for sensorcalibration.

FIG. 38B shows an EIS-assisted sensor calibration flowchart involvinglow start-up detection in accordance with embodiments of the invention.

FIG. 39 shows sensor current (Isig) and 1 kHz impedance magnitude for anin-vitro simulation of an interferent being in close proximity to asensor in accordance with embodiments of the invention.

FIGS. 40A and 40B show Bode plots for phase and impedance, respectively,for the simulation shown in FIG. 39.

FIG. 40C shows a Nyquist plot for the simulation shown in FIG. 39.

FIG. 41 shows another in-vitro simulation with an interferent inaccordance to embodiments of the invention.

FIGS. 42A and 42B illustrate an ASIC block diagram in accordance withembodiments of the invention.

FIG. 43 shows a potentiostat configuration for a sensor with redundantworking electrodes in accordance with embodiments of the invention.

FIG. 44 shows an equivalent AC inter-electrode circuit for a sensor withthe potentiostat configuration shown in FIG. 43.

FIG. 45 shows some of the main blocks of the EIS circuitry in the analogfront end IC of a glucose sensor in accordance with embodiments of theinvention.

FIGS. 46A-46F show a simulation of the signals of the EIS circuitryshown in FIG. 45 for a current of 0-degree phase with a 0-degree phasemultiply.

FIGS. 47A-47F show a simulation of the signals of the EIS circuitryshown in FIG. 45 for a current of 0-degree phase with a 90-degree phasemultiply.

FIG. 48 shows a circuit model in accordance with embodiments of theinvention.

FIGS. 49A-49C show illustrations of circuit models in accordance withalternative embodiments of the invention.

FIG. 50A is a Nyquist plot overlaying an equivalent circuit simulationin accordance with embodiments of the invention.

FIG. 50B is an enlarged diagram of the high-frequency portion of FIG.50A.

FIG. 51 shows a Nyquist plot with increasing Cdl in the direction ofArrow A, in accordance with embodiments of the invention.

FIG. 52 shows a Nyquist plot with increasing a in the direction of ArrowA, in accordance with embodiments of the invention.

FIG. 53 shows a Nyquist plot with increasing Rp in the direction ofArrow A, in accordance with embodiments of the invention.

FIG. 54 shows a Nyquist plot with increasing Warburg admittance in thedirection of Arrow A, in accordance with embodiments of the invention.

FIG. 55 shows a Nyquist plot with increasing λ in the direction of ArrowA, in accordance with embodiments of the invention.

FIG. 56 shows the effect of membrane capacitance on the Nyquist plot, inaccordance with embodiments of the invention.

FIG. 57 shows a Nyquist plot with increasing membrane resistance in thedirection of Arrow A, in accordance with embodiments of the invention.

FIG. 58 shows a Nyquist plot with increasing Rsol in the direction ofArrow A, in accordance with embodiments of the invention.

FIGS. 59A-59C show changes in EIS parameters relating to circuitelements during start-up and calibration in accordance with embodimentsof the invention.

FIGS. 60A-60C show changes in a different set of EIS parameters relatingto circuit elements during start-up and calibration in accordance withembodiments of the invention.

FIGS. 61A-61C show changes in yet a different set of EIS parametersrelating to circuit elements during start-up and calibration inaccordance with embodiments of the invention.

FIG. 62 shows the EIS response for multiple electrodes in accordancewith embodiments of the invention.

FIG. 63 is a Nyquist plot showing the effect of Isig calibration via anincrease in glucose in accordance with embodiments of the invention.

FIG. 64 shows the effect of oxygen (Vcntr) response on the Nyquist plot,in accordance with embodiments of the invention.

FIG. 65 shows a shift in the Nyquist plot due to temperature changes, inaccordance with embodiments of the invention.

FIG. 66 shows the relationship between Isig and blood glucose inaccordance with embodiments of the invention.

FIGS. 67A-67B show sensor drift in accordance with embodiments of theinvention.

FIG. 68 shows an increase in membrane resistance during sensitivityloss, in accordance with embodiments of the invention.

FIG. 69 shows a drop in Warburg Admittance during sensitivity loss, inaccordance with embodiments of the invention.

FIG. 70 shows calibration curves in accordance with embodiments of theinvention.

FIG. 71 shows a higher-frequency semicircle becoming visible on aNyquist plot in accordance with embodiments of the invention.

FIGS. 72A and 72B show Vcntr rail and Cdl decrease in accordance withembodiments of the invention.

FIG. 73 shows the changing slope of calibration curves in accordancewith embodiments of the invention

FIG. 74 shows the changing length of the Nyquist plot in accordance withembodiments of the invention.

FIG. 75 shows enlarged views of the lower-frequency and thehigher-frequency regions of the Nyquist plot of FIG. 74.

FIGS. 76A and 76B show the combined effect of increase in membraneresistance, decrease in Cdl, and Vcntr rail in accordance withembodiments of the invention.

FIG. 77 shows relative Cdl values for two working electrodes inaccordance with embodiments of the invention.

FIG. 78 shows relative Rp values for two working electrodes inaccordance with embodiments of the invention.

FIG. 79 shows the combined effect of changing EIS parameters oncalibration curves in accordance with embodiments of the invention.

FIG. 80 shows that, in accordance with embodiments of the invention, thelength of the Nyquist plot in the lower-frequency region is longer wherethere is sensitivity loss.

FIG. 81 is a flow diagram for sensor self-calibration based on thedetection of sensitivity change in accordance with embodiments of theinvention.

FIG. 82 illustrates a horizontal shift in Nyquist plot as a result ofsensitivity loss, in accordance with embodiments of the invention.

FIG. 83 shows a method of developing a heuristic EIS metric based on aNyquist plot in accordance with embodiments of the invention.

FIG. 84 shows the relationship between Rm and Calibration Factor inaccordance with embodiments of the invention.

FIG. 85 shows the relationship between Rm and normalized Isig inaccordance with embodiments of the invention.

FIG. 86 shows Isig plots for various glucose levels as a function oftime, in accordance with embodiments of the invention.

FIG. 87 shows Cdl plots for various glucose levels as a function oftime, in accordance with embodiments of the invention.

FIG. 88 shows a second inflection point for the plots of FIG. 86, inaccordance with embodiments of the invention.

FIG. 89 shows a second inflection point for Rm corresponding to the peakin FIG. 88, in accordance with embodiments of the invention.

FIG. 90 shows one illustration of the relationship between CalibrationFactor (CF) and Rmem+Rsol in accordance with embodiments of theinvention.

FIG. 91A is a chart showing in-vivo results for MARD over all valid BGsin approximately the first 8 hours of sensor life, in accordance withembodiments of the invention.

FIG. 91B is a chart showing median ARD numbers over all valid BGs inapproximately the first 8 hours of sensor life, in accordance withembodiments of the invention.

FIGS. 92A-92C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIGS. 93A-93C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIGS. 94A-94C show Calibration Factor adjustment in accordance withembodiments of the invention.

FIG. 95 shows an illustrative example of initial decay in Cdl inaccordance with embodiments of the invention.

FIG. 96 shows the effects on Isig of removal of the non-Faradaiccurrent, in accordance with embodiments of the invention.

FIG. 97A shows the Calibration Factor before removal of the non-Faradaiccurrent for two working electrodes, in accordance with embodiments ofthe invention.

FIG. 97B shows the Calibration Factor after removal of the non-Faradaiccurrent for two working electrodes, in accordance with embodiments ofthe invention.

FIGS. 98A and 98B show the effect on MARD of the removal of thenon-Faradaic current, in accordance with embodiments of the invention.

FIG. 99 is an illustration of double layer capacitance over time, inaccordance with embodiments of the invention.

FIG. 100 shows a shift in Rmem+Rsol and the appearance of thehigher-frequency semicircle during sensitivity loss, in accordance withembodiments of the invention.

FIG. 101A shows a flow diagram for detection of sensitivity loss usingcombinatory logic, in accordance with an embodiment of the invention.

FIG. 101B shows a flow diagram for detection of sensitivity loss usingcombinatory logic, in accordance with another embodiment of theinvention.

FIG. 102 shows an illustrative method for using Nyquist slope as amarker to differentiate between new and used sensors, in accordance withembodiments of the invention.

FIGS. 103A-103C show an illustrative example of Nyquist plots havingdifferent lengths for different sensor configurations, in accordancewith embodiments of the invention.

FIG. 104 shows Nyquist plot length as a function of time, for thesensors of FIGS. 103A-103C.

FIG. 105 shows a flow diagram for blanking sensor data or terminating asensor in accordance with an embodiment of the invention.

FIG. 106 shows a flow diagram for sensor termination in accordance withan embodiment of the invention.

FIG. 107 shows a flow diagram for signal dip detection in accordancewith an embodiment of the invention.

FIG. 108A shows Isig and Vcntr as a function of time, and FIG. 108Bshows glucose as a function of time, in accordance with an embodiment ofthe invention.

FIG. 109A calibration ratio as a function of time, and FIG. 109B showglucose as a function of time, in accordance with an embodiment of theinvention.

FIGS. 110A and 110B show calibration factor trends as a function of timein accordance with embodiments of the invention.

FIG. 111 shows a flow diagram for First Day Calibration (FDC) inaccordance with an embodiment of the invention.

FIG. 112 shows a flow diagram for EIS-based calibration in accordancewith an embodiment of the invention.

FIG. 113 shows a flow diagram for an existing calibration methodology.

FIG. 114 shows a calibration flow diagram in accordance with embodimentsof the invention.

FIG. 115 shows a calibration flow diagram in accordance with otherembodiments of the invention.

FIG. 116 shows a calibration flow diagram in accordance with yet otherembodiments of the invention.

FIG. 117 shows a calibration flow diagram in accordance with otherembodiments of the invention.

FIG. 118 shows a table of comparative MARD values calculated based onembodiments of the invention.

FIG. 119 shows a flow diagram for calculation of raw fusion weights inaccordance with embodiments of the invention.

FIG. 120 shows a Sensor Glucose (SG) fusion logic diagram in accordancewith embodiments of the invention.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawings which form a part hereof and which illustrate severalembodiments of the present inventions. It is understood that otherembodiments may be utilized and structural and operational changes maybe made without departing from the scope of the present inventions.

The inventions herein are described below with reference to flowchartillustrations of methods, systems, devices, apparatus, and programmingand computer program products. It will be understood that each block ofthe flowchart illustrations, and combinations of blocks in the flowchartillustrations, can be implemented by programming instructions, includingcomputer program instructions (as can any menu screens described in thefigures). These computer program instructions may be loaded onto acomputer or other programmable data processing apparatus (such as acontroller, microcontroller, or processor in a sensor electronicsdevice) to produce a machine, such that the instructions which executeon the computer or other programmable data processing apparatus createinstructions for implementing the functions specified in the flowchartblock or blocks. These computer program instructions may also be storedin a computer-readable memory that can direct a computer or otherprogrammable data processing apparatus to function in a particularmanner, such that the instructions stored in the computer-readablememory produce an article of manufacture including instructions whichimplement the function specified in the flowchart block or blocks. Thecomputer program instructions may also be loaded onto a computer orother programmable data processing apparatus to cause a series ofoperational steps to be performed on the computer or other programmableapparatus to produce a computer implemented process such that theinstructions which execute on the computer or other programmableapparatus provide steps for implementing the functions specified in theflowchart block or blocks, and/or menus presented herein. Programminginstructions may also be stored in and/or implemented via electroniccircuitry, including integrated circuits (ICs) and Application SpecificIntegrated Circuits (ASICs) used in conjunction with sensor devices,apparatuses, and systems.

FIG. 1 is a perspective view of a subcutaneous sensor insertion set anda block diagram of a sensor electronics device according to anembodiment of the invention. As illustrated in FIG. 1, a subcutaneoussensor set 10 is provided for subcutaneous placement of an activeportion of a flexible sensor 12 (see, e.g., FIG. 2), or the like, at aselected site in the body of a user. The subcutaneous or percutaneousportion of the sensor set 10 includes a hollow, slotted insertion needle14, and a cannula 16. The needle 14 is used to facilitate quick and easysubcutaneous placement of the cannula 16 at the subcutaneous insertionsite. Inside the cannula 16 is a sensing portion 18 of the sensor 12 toexpose one or more sensor electrodes 20 to the user's bodily fluidsthrough a window 22 formed in the cannula 16. In an embodiment of theinvention, the one or more sensor electrodes 20 may include a counterelectrode, a reference electrode, and one or more working electrodes.After insertion, the insertion needle 14 is withdrawn to leave thecannula 16 with the sensing portion 18 and the sensor electrodes 20 inplace at the selected insertion site.

In particular embodiments, the subcutaneous sensor set 10 facilitatesaccurate placement of a flexible thin film electrochemical sensor 12 ofthe type used for monitoring specific blood parameters representative ofa user's condition. The sensor 12 monitors glucose levels in the body,and may be used in conjunction with automated or semi-automatedmedication infusion pumps of the external or implantable type asdescribed, e.g., in U.S. Pat. Nos. 4,562,751; 4,678,408; 4,685,903 or4,573,994, to control delivery of insulin to a diabetic patient.

Particular embodiments of the flexible electrochemical sensor 12 areconstructed in accordance with thin film mask techniques to includeelongated thin film conductors embedded or encased between layers of aselected insulative material such as polyimide film or sheet, andmembranes. The sensor electrodes 20 at a tip end of the sensing portion18 are exposed through one of the insulative layers for direct contactwith patient blood or other body fluids, when the sensing portion 18 (oractive portion) of the sensor 12 is subcutaneously placed at aninsertion site. The sensing portion 18 is joined to a connection portion24 that terminates in conductive contact pads, or the like, which arealso exposed through one of the insulative layers. In alternativeembodiments, other types of implantable sensors, such as chemical based,optical based, or the like, may be used.

As is known in the art, the connection portion 24 and the contact padsare generally adapted for a direct wired electrical connection to asuitable monitor or sensor electronics device 100 for monitoring auser's condition in response to signals derived from the sensorelectrodes 20. Further description of flexible thin film sensors of thisgeneral type are be found in U.S. Pat. No. 5,391,250, entitled METHOD OFFABRICATING THIN FILM SENSORS, which is herein incorporated byreference. The connection portion 24 may be conveniently connectedelectrically to the monitor or sensor electronics device 100 or by aconnector block 28 (or the like) as shown and described in U.S. Pat. No.5,482,473, entitled FLEX CIRCUIT CONNECTOR, which is also hereinincorporated by reference. Thus, in accordance with embodiments of thepresent invention, subcutaneous sensor sets 10 may be configured orformed to work with either a wired or a wireless characteristic monitorsystem.

The sensor electrodes 20 may be used in a variety of sensingapplications and may be configured in a variety of ways. For example,the sensor electrodes 20 may be used in physiological parameter sensingapplications in which some type of biomolecule is used as a catalyticagent. For example, the sensor electrodes 20 may be used in a glucoseand oxygen sensor having a glucose oxidase (GOx) enzyme catalyzing areaction with the sensor electrodes 20. The sensor electrodes 20, alongwith a biomolecule or some other catalytic agent, may be placed in ahuman body in a vascular or non-vascular environment. For example, thesensor electrodes 20 and biomolecule may be placed in a vein and besubjected to a blood stream, or may be placed in a subcutaneous orperitoneal region of the human body.

The monitor 100 may also be referred to as a sensor electronics device100. The monitor 100 may include a power source 110, a sensor interface122, processing electronics 124, and data formatting electronics 128.The monitor 100 may be coupled to the sensor set 10 by a cable 102through a connector that is electrically coupled to the connector block28 of the connection portion 24. In an alternative embodiment, the cablemay be omitted. In this embodiment of the invention, the monitor 100 mayinclude an appropriate connector for direct connection to the connectionportion 104 of the sensor set 10. The sensor set 10 may be modified tohave the connector portion 104 positioned at a different location, e.g.,on top of the sensor set to facilitate placement of the monitor 100 overthe sensor set.

In embodiments of the invention, the sensor interface 122, theprocessing electronics 124, and the data formatting electronics 128 areformed as separate semiconductor chips, however, alternative embodimentsmay combine the various semiconductor chips into a single or multiplecustomized semiconductor chips. The sensor interface 122 connects withthe cable 102 that is connected with the sensor set 10.

The power source 110 may be a battery. The battery can include threeseries silver oxide 357 battery cells. In alternative embodiments,different battery chemistries may be utilized, such as lithium basedchemistries, alkaline batteries, nickel metalhydride, or the like, and adifferent number of batteries may be used. The monitor 100 providespower to the sensor set via the power source 110, through the cable 102and cable connector 104. In an embodiment of the invention, the power isa voltage provided to the sensor set 10. In an embodiment of theinvention, the power is a current provided to the sensor set 10. In anembodiment of the invention, the power is a voltage provided at aspecific voltage to the sensor set 10.

FIGS. 2A and 2B illustrate an implantable sensor and electronics fordriving the implantable sensor according to an embodiment of the presentinvention. FIG. 2A shows a substrate 220 having two sides, a first side222 of which contains an electrode configuration and a second side 224of which contains electronic circuitry. As may be seen in FIG. 2A, afirst side 222 of the substrate comprises two counter electrode-workingelectrode pairs 240, 242, 244, 246 on opposite sides of a referenceelectrode 248. A second side 224 of the substrate comprises electroniccircuitry. As shown, the electronic circuitry may be enclosed in ahermetically sealed casing 226, providing a protective housing for theelectronic circuitry. This allows the sensor substrate 220 to beinserted into a vascular environment or other environment which maysubject the electronic circuitry to fluids. By sealing the electroniccircuitry in a hermetically sealed casing 226, the electronic circuitrymay operate without risk of short circuiting by the surrounding fluids.Also shown in FIG. 2A are pads 228 to which the input and output linesof the electronic circuitry may be connected. The electronic circuitryitself may be fabricated in a variety of ways. According to anembodiment of the present invention, the electronic circuitry may befabricated as an integrated circuit using techniques common in theindustry.

FIG. 2B illustrates a general block diagram of an electronic circuit forsensing an output of a sensor according to an embodiment of the presentinvention. At least one pair of sensor electrodes 310 may interface to adata converter 312, the output of which may interface to a counter 314.The counter 314 may be controlled by control logic 316. The output ofthe counter 314 may connect to a line interface 318. The line interface318 may be connected to input and output lines 320 and may also connectto the control logic 316. The input and output lines 320 may also beconnected to a power rectifier 322.

The sensor electrodes 310 may be used in a variety of sensingapplications and may be configured in a variety of ways. For example,the sensor electrodes 310 may be used in physiological parameter sensingapplications in which some type of biomolecule is used as a catalyticagent. For example, the sensor electrodes 310 may be used in a glucoseand oxygen sensor having a glucose oxidase (GOx) enzyme catalyzing areaction with the sensor electrodes 310. The sensor electrodes 310,along with a biomolecule or some other catalytic agent, may be placed ina human body in a vascular or non-vascular environment. For example, thesensor electrodes 310 and biomolecule may be placed in a vein and besubjected to a blood stream.

FIG. 3 illustrates a block diagram of a sensor electronics device and asensor including a plurality of electrodes according to an embodiment ofthe invention. The sensor set or system 350 includes a sensor 355 and asensor electronics device 360. The sensor 355 includes a counterelectrode 365, a reference electrode 370, and a working electrode 375.The sensor electronics device 360 includes a power supply 380, aregulator 385, a signal processor 390, a measurement processor 395, anda display/transmission module 397. The power supply 380 provides power(in the form of either a voltage, a current, or a voltage including acurrent) to the regulator 385. The regulator 385 transmits a regulatedvoltage to the sensor 355. In an embodiment of the invention, theregulator 385 transmits a voltage to the counter electrode 365 of thesensor 355.

The sensor 355 creates a sensor signal indicative of a concentration ofa physiological characteristic being measured. For example, the sensorsignal may be indicative of a blood glucose reading. In an embodiment ofthe invention utilizing subcutaneous sensors, the sensor signal mayrepresent a level of hydrogen peroxide in a subject. In an embodiment ofthe invention where blood or cranial sensors are utilized, the amount ofoxygen is being measured by the sensor and is represented by the sensorsignal. In an embodiment of the invention utilizing implantable orlong-term sensors, the sensor signal may represent a level of oxygen inthe subject. The sensor signal is measured at the working electrode 375.In an embodiment of the invention, the sensor signal may be a currentmeasured at the working electrode. In an embodiment of the invention,the sensor signal may be a voltage measured at the working electrode.

The signal processor 390 receives the sensor signal (e.g., a measuredcurrent or voltage) after the sensor signal is measured at the sensor355 (e.g., the working electrode). The signal processor 390 processesthe sensor signal and generates a processed sensor signal. Themeasurement processor 395 receives the processed sensor signal andcalibrates the processed sensor signal utilizing reference values. In anembodiment of the invention, the reference values are stored in areference memory and provided to the measurement processor 395. Themeasurement processor 395 generates sensor measurements. The sensormeasurements may be stored in a measurement memory (not shown). Thesensor measurements may be sent to a display/transmission device to beeither displayed on a display in a housing with the sensor electronicsor transmitted to an external device.

The sensor electronics device 360 may be a monitor which includes adisplay to display physiological characteristics readings. The sensorelectronics device 360 may also be installed in a desktop computer, apager, a television including communications capabilities, a laptopcomputer, a server, a network computer, a personal digital assistant(PDA), a portable telephone including computer functions, an infusionpump including a display, a glucose sensor including a display, and/or acombination infusion pump/glucose sensor. The sensor electronics device360 may be housed in a blackberry, a network device, a home networkdevice, or an appliance connected to a home network.

FIG. 4 illustrates an alternative embodiment of the invention includinga sensor and a sensor electronics device according to an embodiment ofthe invention. The sensor set or sensor system 400 includes a sensorelectronics device 360 and a sensor 355. The sensor includes a counterelectrode 365, a reference electrode 370, and a working electrode 375.The sensor electronics device 360 includes a microcontroller 410 and adigital-to-analog converter (DAC) 420. The sensor electronics device 360may also include a current-to-frequency converter (I/F converter) 430.

The microcontroller 410 includes software program code, which whenexecuted, or programmable logic which, causes the microcontroller 410 totransmit a signal to the DAC 420, where the signal is representative ofa voltage level or value that is to be applied to the sensor 355. TheDAC 420 receives the signal and generates the voltage value at the levelinstructed by the microcontroller 410. In embodiments of the invention,the microcontroller 410 may change the representation of the voltagelevel in the signal frequently or infrequently. Illustratively, thesignal from the microcontroller 410 may instruct the DAC 420 to apply afirst voltage value for one second and a second voltage value for twoseconds.

The sensor 355 may receive the voltage level or value. In an embodimentof the invention, the counter electrode 365 may receive the output of anoperational amplifier which has as inputs the reference voltage and thevoltage value from the DAC 420. The application of the voltage levelcauses the sensor 355 to create a sensor signal indicative of aconcentration of a physiological characteristic being measured. In anembodiment of the invention, the microcontroller 410 may measure thesensor signal (e.g., a current value) from the working electrode.Illustratively, a sensor signal measurement circuit 431 may measure thesensor signal. In an embodiment of the invention, the sensor signalmeasurement circuit 431 may include a resistor and the current may bepassed through the resistor to measure the value of the sensor signal.In an embodiment of the invention, the sensor signal may be a currentlevel signal and the sensor signal measurement circuit 431 may be acurrent-to-frequency (I/F) converter 430. The current-to-frequencyconverter 430 may measure the sensor signal in terms of a currentreading, convert it to a frequency-based sensor signal, and transmit thefrequency-based sensor signal to the microcontroller 410. In embodimentsof the invention, the microcontroller 410 may be able to receivefrequency-based sensor signals easier than non-frequency-based sensorsignals. The microcontroller 410 receives the sensor signal, whetherfrequency-based or non frequency-based, and determines a value for thephysiological characteristic of a subject, such as a blood glucoselevel. The microcontroller 410 may include program code, which whenexecuted or run, is able to receive the sensor signal and convert thesensor signal to a physiological characteristic value. In an embodimentof the invention, the microcontroller 410 may convert the sensor signalto a blood glucose level. In an embodiment of the invention, themicrocontroller 410 may utilize measurements stored within an internalmemory in order to determine the blood glucose level of the subject. Inan embodiment of the invention, the microcontroller 410 may utilizemeasurements stored within a memory external to the microcontroller 410to assist in determining the blood glucose level of the subject.

After the physiological characteristic value is determined by themicrocontroller 410, the microcontroller 410 may store measurements ofthe physiological characteristic values for a number of time periods.For example, a blood glucose value may be sent to the microcontroller410 from the sensor every second or five seconds, and themicrocontroller may save sensor measurements for five minutes or tenminutes of BG readings. The microcontroller 410 may transfer themeasurements of the physiological characteristic values to a display onthe sensor electronics device 360. For example, the sensor electronicsdevice 360 may be a monitor which includes a display that provides ablood glucose reading for a subject. In an embodiment of the invention,the microcontroller 410 may transfer the measurements of thephysiological characteristic values to an output interface of themicrocontroller 410. The output interface of the microcontroller 410 maytransfer the measurements of the physiological characteristic values,e.g., blood glucose values, to an external device, e.g., an infusionpump, a combined infusion pump/glucose meter, a computer, a personaldigital assistant, a pager, a network appliance, a server, a cellularphone, or any computing device.

FIG. 5 illustrates an electronic block diagram of the sensor electrodesand a voltage being applied to the sensor electrodes according to anembodiment of the present invention. In the embodiment of the inventionillustrated in FIG. 5, an op amp 530 or other servo controlled devicemay connect to sensor electrodes 510 through a circuit/electrodeinterface 538. The op amp 530, utilizing feedback through the sensorelectrodes, attempts to maintain a prescribed voltage (what the DAC maydesire the applied voltage to be) between a reference electrode 532 anda working electrode 534 by adjusting the voltage at a counter electrode536. Current may then flow from a counter electrode 536 to a workingelectrode 534. Such current may be measured to ascertain theelectrochemical reaction between the sensor electrodes 510 and thebiomolecule of a sensor that has been placed in the vicinity of thesensor electrodes 510 and used as a catalyzing agent. The circuitrydisclosed in FIG. 5 may be utilized in a long-term or implantable sensoror may be utilized in a short-term or subcutaneous sensor.

In a long-term sensor embodiment, where a glucose oxidase (GOx) enzymeis used as a catalytic agent in a sensor, current may flow from thecounter electrode 536 to a working electrode 534 only if there is oxygenin the vicinity of the enzyme and the sensor electrodes 510.Illustratively, if the voltage set at the reference electrode 532 ismaintained at about 0.5 volts, the amount of current flowing from thecounter electrode 536 to a working electrode 534 has a fairly linearrelationship with unity slope to the amount of oxygen present in thearea surrounding the enzyme and the electrodes. Thus, increased accuracyin determining an amount of oxygen in the blood may be achieved bymaintaining the reference electrode 532 at about 0.5 volts and utilizingthis region of the current-voltage curve for varying levels of bloodoxygen. Different embodiments of the present invention may utilizedifferent sensors having biomolecules other than a glucose oxidaseenzyme and may, therefore, have voltages other than 0.5 volts set at thereference electrode.

As discussed above, during initial implantation or insertion of thesensor 510, the sensor 510 may provide inaccurate readings due to theadjusting of the subject to the sensor and also electrochemicalbyproducts caused by the catalyst utilized in the sensor. Astabilization period is needed for many sensors in order for the sensor510 to provide accurate readings of the physiological parameter of thesubject. During the stabilization period, the sensor 510 does notprovide accurate blood glucose measurements. Users and manufacturers ofthe sensors may desire to improve the stabilization timeframe for thesensor so that the sensors can be utilized quickly after insertion intothe subject's body or a subcutaneous layer of the subject.

In previous sensor electrode systems, the stabilization period ortimeframe was one hour to three hours. In order to decrease thestabilization period or timeframe and increase the timeliness ofaccuracy of the sensor, a sensor (or electrodes of a sensor) may besubjected to a number of pulses rather than the application of one pulsefollowed by the application of another voltage. FIG. 6A illustrates amethod of applying pulses during a stabilization timeframe in order toreduce the stabilization timeframe according to an embodiment of thepresent invention. In this embodiment of the invention, a voltageapplication device applies 600 a first voltage to an electrode for afirst time or time period. In an embodiment of the invention, the firstvoltage may be a DC constant voltage. This results in an anodic currentbeing generated. In an alternative embodiment of the invention, adigital-to-analog converter or another voltage source may supply thevoltage to the electrode for a first time period. The anodic currentmeans that electrons are being driven towards the electrode to which thevoltage is applied. In an embodiment of the invention, an applicationdevice may apply a current instead of a voltage. In an embodiment of theinvention where a voltage is applied to a sensor, after the applicationof the first voltage to the electrode, the voltage regulator may wait(i.e., not apply a voltage) for a second time, timeframe, or time period605. In other words, the voltage application device waits until a secondtime period elapses. The non-application of voltage results in acathodic current, which results in the gaining of electrons by theelectrode to which the voltage is not applied. The application of thefirst voltage to the electrode for a first time period followed by thenon-application of voltage for a second time period is repeated 610 fora number of iterations. This may be referred to as an anodic andcathodic cycle. In an embodiment of the invention, the number of totaliterations of the stabilization method is three, i.e., threeapplications of the voltage for the first time period, each followed byno application of the voltage for the second time period. In anembodiment of the invention, the first voltage may be 1.07 volts. In anembodiment of the invention, the first voltage may be 0.535 volts. In anembodiment of the invention, the first voltage may be approximately 0.7volts.

The repeated application of the voltage and the non-application of thevoltage results in the sensor (and thus the electrodes) being subjectedto an anodic-cathodic cycle. The anodic-cathodic cycle results in thereduction of electrochemical byproducts which are generated by apatient's body reacting to the insertion of the sensor or the implantingof the sensor. In an embodiment of the invention, the electrochemicalbyproducts cause generation of a background current, which results ininaccurate measurements of the physiological parameter of the subject.In an embodiment of the invention, the electrochemical byproduct may beeliminated. Under other operating conditions, the electrochemicalbyproducts may be reduced or significantly reduced. A successfulstabilization method results in the anodic-cathodic cycle reachingequilibrium, electrochemical byproducts being significantly reduced, andbackground current being minimized.

In an embodiment of the invention, the first voltage being applied tothe electrode of the sensor may be a positive voltage. In an embodimentof the invention, the first voltage being applied may be a negativevoltage. In an embodiment of the invention, the first voltage may beapplied to a working electrode. In an embodiment of the invention, thefirst voltage may be applied to the counter electrode or the referenceelectrode.

In embodiments of the invention, the duration of the voltage pulse andthe non-application of voltage may be equal, e.g., such as three minuteseach. In embodiments of the invention, the duration of the voltageapplication or voltage pulse may be different values, e.g., the firsttime and the second time may be different. In an embodiment of theinvention, the first time period may be five minutes and the waitingperiod may be two minutes. In an embodiment of the invention, the firsttime period may be two minutes and the waiting period (or secondtimeframe) may be five minutes. In other words, the duration for theapplication of the first voltage may be two minutes and there may be novoltage applied for five minutes. This timeframe is only meant to beillustrative and should not be limiting. For example, a first timeframemay be two, three, five or ten minutes and the second timeframe may befive minutes, ten minutes, twenty minutes, or the like. The timeframes(e.g., the first time and the second time) may depend on uniquecharacteristics of different electrodes, the sensors, and/or thepatient's physiological characteristics.

In embodiments of the invention, more or less than three pulses may beutilized to stabilize the glucose sensor. In other words, the number ofiterations may be greater than 3 or less than three. For example, fourvoltage pulses (e.g., a high voltage followed by no voltage) may beapplied to one of the electrodes or six voltage pulses may be applied toone of the electrodes.

Illustratively, three consecutive pulses of 1.07 volts (followed byrespective waiting periods) may be sufficient for a sensor implantedsubcutaneously. In an embodiment of the invention, three consecutivevoltage pulses of 0.7 volts may be utilized. The three consecutivepulses may have a higher or lower voltage value, either negative orpositive, for a sensor implanted in blood or cranial fluid, e.g., thelong-term or permanent sensors. In addition, more than three pulses(e.g., five, eight, twelve) may be utilized to create theanodic-cathodic cycling between anodic and cathodic currents in any ofthe subcutaneous, blood, or cranial fluid sensors.

FIG. 6B illustrates a method of stabilizing sensors according to anembodiment of the invention. In the embodiment of the inventionillustrated in FIG. 6B, a voltage application device may apply 630 afirst voltage to the sensor for a first time to initiate an anodic cycleat an electrode of the sensor. The voltage application device may be aDC power supply, a digital-to-analog converter, or a voltage regulator.After the first time period has elapsed, a second voltage is applied 635to the sensor for a second time to initiate a cathodic cycle at anelectrode of the sensor. Illustratively, rather than no voltage beingapplied, as is illustrated in the method of FIG. 6A, a different voltage(from the first voltage) is applied to the sensor during the secondtimeframe. In an embodiment of the invention, the application of thefirst voltage for the first time and the application of the secondvoltage for the second time is repeated 640 for a number of iterations.In an embodiment of the invention, the application of the first voltagefor the first time and the application of the second voltage for thesecond time may each be applied for a stabilization timeframe, e.g., 10minutes, 15 minutes, or 20 minutes rather than for a number ofiterations. This stabilization timeframe is the entire timeframe for thestabilization sequence, e.g., until the sensor (and electrodes) arestabilized. The benefit of this stabilization methodology is a fasterrun-in of the sensors, less background current (in other words asuppression of some the background current), and a better glucoseresponse.

In an embodiment of the invention, the first voltage may be 0.535 voltsapplied for five minutes, the second voltage may be 1.070 volts appliedfor two minutes, the first voltage of 0.535 volts may be applied forfive minutes, the second voltage of 1.070 volts may be applied for twominutes, the first voltage of 0.535 volts may be applied for fiveminutes, and the second voltage of 1.070 volts may be applied for twominutes. In other words, in this embodiment, there are three iterationsof the voltage pulsing scheme. The pulsing methodology may be changed inthat the second timeframe, e.g., the timeframe of the application of thesecond voltage may be lengthened from two minutes to five minutes, tenminutes, fifteen minutes, or twenty minutes. In addition, after thethree iterations are applied in this embodiment of the invention, anominal working voltage of 0.535 volts may be applied.

The 1.070 and 0.535 volts are illustrative values. Other voltage valuesmay be selected based on a variety of factors. These factors may includethe type of enzyme utilized in the sensor, the membranes utilized in thesensor, the operating period of the sensor, the length of the pulse,and/or the magnitude of the pulse. Under certain operating conditions,the first voltage may be in a range of 1.00 to 1.09 volts and the secondvoltage may be in a range of 0.510 to 0.565 volts. In other operatingembodiments, the ranges that bracket the first voltage and the secondvoltage may have a higher range, e.g., 0.3 volts, 0.6 volts, 0.9 volts,depending on the voltage sensitivity of the electrode in the sensor.Under other operating conditions, the voltage may be in a range of 0.8volts to 1.34 volts and the other voltage may be in a range of 0.335 to0.735. Under other operating conditions, the range of the higher voltagemay be smaller than the range of the lower voltage. Illustratively, thehigher voltage may be in a range of 0.9 to 1.09 volts and the lowervoltage may be in a range of 0.235 to 0.835 volts.

In an embodiment of the invention, the first voltage and the secondvoltage may be positive voltages, or alternatively in other embodimentsof the invention, negative voltages. In an embodiment of the invention,the first voltage may be positive and the second voltage may benegative, or alternatively, the first voltage may be negative and thesecond voltage may be positive. The first voltage may be differentvoltage levels for each of the iterations. In an embodiment of theinvention, the first voltage may be a D.C. constant voltage. In otherembodiments of the invention, the first voltage may be a ramp voltage, asinusoid-shaped voltage, a stepped voltage, or other commonly utilizedvoltage waveforms. In an embodiment of the invention, the second voltagemay be a D.C. constant voltage, a ramp voltage, a sinusoid-shapedvoltage, a stepped voltage, or other commonly utilized voltagewaveforms. In an embodiment of the invention, the first voltage or thesecond voltage may be an AC signal riding on a DC waveform. In anembodiment of the invention, the first voltage may be one type ofvoltage, e.g., a ramp voltage, and the second voltage may be a secondtype of voltage, e.g., a sinusoid-shaped voltage. In an embodiment ofthe invention, the first voltage (or the second voltage) may havedifferent waveform shapes for each of the iterations. For example, ifthere are three cycles in a stabilization method, in a first cycle, thefirst voltage may be a ramp voltage, in the second cycle, the firstvoltage may be a constant voltage, and in the third cycle, the firstvoltage may be a sinusoidal voltage.

In an embodiment of the invention, a duration of the first timeframe anda duration of the second timeframe may have the same value, oralternatively, the duration of the first timeframe and the secondtimeframe may have different values. For example, the duration of thefirst timeframe may be two minutes and the duration of the secondtimeframe may be five minutes and the number of iterations may be three.As discussed above, the stabilization method may include a number ofiterations. In embodiments of the invention, during different iterationsof the stabilization method, the duration of each of the firsttimeframes may change and the duration of each of the second timeframesmay change. Illustratively, during the first iteration of theanodic-cathodic cycling, the first timeframe may be 2 minutes and thesecond timeframe may be 5 minutes. During the second iteration, thefirst timeframe may be 1 minute and the second timeframe may be 3minutes. During the third iteration, the first timeframe may be 3minutes and the second timeframe may be 10 minutes.

In an embodiment of the invention, a first voltage of 0.535 volts isapplied to an electrode in a sensor for two minutes to initiate ananodic cycle, then a second voltage of 1.07 volts is applied to theelectrode for five minutes to initiate a cathodic cycle. The firstvoltage of 0.535 volts is then applied again for two minutes to initiatethe anodic cycle and a second voltage of 1.07 volts is applied to thesensor for five minutes. In a third iteration, 0.535 volts is appliedfor two minutes to initiate the anodic cycle and then 1.07 volts isapplied for five minutes. The voltage applied to the sensor is then0.535 during the actual working timeframe of the sensor, e.g., when thesensor provides readings of a physiological characteristic of a subject.

Shorter duration voltage pulses may be utilized in the embodiment ofFIGS. 6A and 6B. The shorter duration voltage pulses may be utilized toapply the first voltage, the second voltage, or both. In an embodimentof the present invention, the magnitude of the shorter duration voltagepulse for the first voltage is −1.07 volts and the magnitude of theshorter duration voltage pulse for the second voltage is approximatelyhalf of the high magnitude, e.g., −0.535 volts. Alternatively, themagnitude of the shorter duration pulse for the first voltage may be0.535 volts and the magnitude of the shorter duration pulse for thesecond voltage is 1.07 volts.

In embodiments of the invention utilizing short duration pulses, thevoltage may not be applied continuously for the entire first timeperiod. Instead, the voltage application device may transmit a number ofshort duration pulses during the first time period. In other words, anumber of mini-width or short duration voltage pulses may be applied tothe electrodes of the sensor over the first time period. Each mini-widthor short duration pulse may have a width of a number of milliseconds.Illustratively, this pulse width may be 30 milliseconds, 50milliseconds, 70 milliseconds or 200 milliseconds. These values aremeant to be illustrative and not limiting. In an embodiment of theinvention, such as the embodiment illustrated in FIG. 6A, these shortduration pulses are applied to the sensor (electrode) for the first timeperiod and then no voltage is applied for the second time period.

In an embodiment of the invention, each short duration pulse may havethe same time duration within the first time period. For example, eachshort duration voltage pulse may have a time width of 50 millisecondsand each pulse delay between the pulses may be 950 milliseconds. In thisexample, if two minutes is the measured time for the first timeframe,then 120 short duration voltage pulses may be applied to the sensor. Inan embodiment of the invention, each of the short duration voltagepulses may have different time durations. In an embodiment of theinvention, each of the short duration voltage pulses may have the sameamplitude values. In an embodiment of the invention, each of the shortduration voltage pulses may have different amplitude values. Byutilizing short duration voltage pulses rather than a continuousapplication of voltage to the sensor, the same anodic and cathodiccycling may occur and the sensor (e.g., electrodes) is subjected to lesstotal energy or charge over time. The use of short duration voltagepulses utilizes less power as compared to the application of continuousvoltage to the electrodes because there is less energy applied to thesensors (and thus the electrodes).

FIG. 6C illustrates utilization of feedback in stabilizing the sensoraccording to an embodiment of the present invention. The sensor systemmay include a feedback mechanism to determine if additional pulses areneeded to stabilize a sensor. In an embodiment of the invention, asensor signal generated by an electrode (e.g., a working electrode) maybe analyzed to determine if the sensor signal is stabilized. A firstvoltage is applied 630 to an electrode for a first timeframe to initiatean anodic cycle. A second voltage is applied 635 to an electrode for asecond timeframe to initiate a cathodic cycle. In an embodiment of theinvention, an analyzation module may analyze a sensor signal (e.g., thecurrent emitted by the sensor signal, a resistance at a specific pointin the sensor, an impedance at a specific node in the sensor) anddetermine if a threshold measurement has been reached 637 (e.g.,determining if the sensor is providing accurate readings by comparingagainst the threshold measurement). If the sensor readings aredetermined to be accurate, which represents that the electrode (and thusthe sensor) is stabilized 642, no additional application of the firstvoltage and/or the second voltage may be generated. If stability was notachieved, in an embodiment of the invention, then an additionalanodic/cathodic cycle is initiated by the application 630 of a firstvoltage to an electrode for a first time period and then the application635 of the second voltage to the electrode for a second time period.

In embodiments of the invention, the analyzation module may be employedafter an anodic/cathodic cycle of three applications of the firstvoltage and the second voltage to an electrode of the sensor. In anembodiment of the invention, an analyzation module may be employed afterone application of the first voltage and the second voltage, as isillustrated in FIG. 6C.

In an embodiment of the invention, the analyzation module may beutilized to measure a voltage emitted after a current has beenintroduced across an electrode or across two electrodes. The analyzationmodule may monitor a voltage level at the electrode or at the receivinglevel. In an embodiment of the invention, if the voltage level is abovea certain threshold, this may mean that the sensor is stabilized. In anembodiment of the invention, if the voltage level falls below athreshold level, this may indicate that the sensor is stabilized andready to provide readings. In an embodiment of the invention, a currentmay be introduced to an electrode or across a couple of electrodes. Theanalyzation module may monitor a current level emitted from theelectrode. In this embodiment of the invention, the analyzation modulemay be able to monitor the current if the current is different by anorder of magnitude from the sensor signal current. If the current isabove or below a current threshold, this may signify that the sensor isstabilized.

In an embodiment of the invention, the analyzation module may measure animpedance between two electrodes of the sensor. The analyzation modulemay compare the impedance against a threshold or target impedance valueand if the measured impedance is lower than the target or thresholdimpedance, the sensor (and hence the sensor signal) may be stabilized.In an embodiment of the invention, the analyzation module may measure aresistance between two electrodes of the sensor. In this embodiment ofthe invention, if the analyzation module compares the resistance againsta threshold or target resistance value and the measured resistance valueis less than the threshold or target resistance value, then theanalyzation module may determine that the sensor is stabilized and thatthe sensor signal may be utilized.

FIG. 7 illustrates an effect of stabilizing a sensor according to anembodiment of the invention. Line 705 represents blood glucose sensorreadings for a glucose sensor where a previous single pulsestabilization method was utilized. Line 710 represents blood glucosereadings for a glucose sensor where three voltage pulses are applied(e.g., 3 voltage pulses having a duration of 2 minutes each followed by5 minutes of no voltage being applied). The x-axis 715 represents anamount of time. The dots 720, 725, 730, and 735 represent measuredglucose readings, taken utilizing a finger stick and then input into aglucose meter. As illustrated by the graph, the previous single pulsestabilization method took approximately 1 hour and 30 minutes in orderto stabilize to the desired glucose reading, e.g., 100 units. Incontrast, the three pulse stabilization method took only approximately15 minutes to stabilize the glucose sensor and results in a drasticallyimproved stabilization timeframe.

FIG. 8A illustrates a block diagram of a sensor electronics device and asensor including a voltage generation device according to an embodimentof the invention. The voltage generation or application device 810includes electronics, logic, or circuits which generate voltage pulses.The sensor electronics device 360 may also include an input device 820to receive reference values and other useful data. In an embodiment ofthe invention, the sensor electronics device may include a measurementmemory 830 to store sensor measurements. In this embodiment of theinvention, the power supply 380 may supply power to the sensorelectronics device. The power supply 380 may supply power to a regulator385, which supplies a regulated voltage to the voltage generation orapplication device 810. The connection terminals 811 represent that inthe illustrated embodiment of the invention, the connection terminalcouples or connects the sensor 355 to the sensor electronics device 360.

In an embodiment of the invention illustrated in FIG. 8A, the voltagegeneration or application device 810 supplies a voltage, e.g., the firstvoltage or the second voltage, to an input terminal of an operationalamplifier 840. The voltage generation or application device 810 may alsosupply the voltage to a working electrode 375 of the sensor 355. Anotherinput terminal of the operational amplifier 840 is coupled to thereference electrode 370 of the sensor. The application of the voltagefrom the voltage generation or application device 810 to the operationalamplifier 840 drives a voltage measured at the counter electrode 365 tobe close to or equal to the voltage applied at the working electrode375. In an embodiment of the invention, the voltage generation orapplication device 810 could be utilized to apply the desired voltagebetween the counter electrode and the working electrode. This may occurby the application of the fixed voltage to the counter electrodedirectly.

In an embodiment of the invention as illustrated in FIGS. 6A and 6B, thevoltage generation device 810 generates a first voltage that is to beapplied to the sensor during a first timeframe. The voltage generationdevice 810 transmits this first voltage to an op amp 840 which drivesthe voltage at a counter electrode 365 of the sensor 355 to the firstvoltage. In an embodiment of the invention, the voltage generationdevice 810 also could transmit the first voltage directly to the counterelectrode 365 of the sensor 355. In the embodiment of the inventionillustrated in FIG. 6A, the voltage generation device 810 then does nottransmit the first voltage to the sensor 355 for a second timeframe. Inother words, the voltage generation device 810 is turned off or switchedoff. The voltage generation device 810 may be programmed to continuecycling between applying the first voltage and not applying a voltagefor either a number of iterations or for a stabilization timeframe,e.g., for twenty minutes. FIG. 8B illustrates a voltage generationdevice to implement this embodiment of the invention. The voltageregulator 385 transfers the regulated voltage to the voltage generationdevice 810. A control circuit 860 controls the closing and opening of aswitch 850. If the switch 850 is closed, the voltage is applied. If theswitch 850 is opened, the voltage is not applied. The timer 865 providesa signal to the control circuit 860 to instruct the control circuit 860to turn on and off the switch 850. The control circuit 860 includeslogic which can instruct the circuit to open and close the switch 850 anumber of times (to match the necessary iterations). In an embodiment ofthe invention, the timer 865 may also transmit a stabilization signal toidentify that the stabilization sequence is completed, i.e., that astabilization timeframe has elapsed.

In an embodiment of the invention, the voltage generation devicegenerates a first voltage for a first timeframe and generates a secondvoltage for a second timeframe. FIG. 8C illustrates a voltage generationdevice to generate two voltage values to implement this embodiment ofthe invention. In this embodiment of the invention, a two positionswitch 870 is utilized. Illustratively, if the first switch position 871is turned on or closed by the timer 865 instructing the control circuit860, then the voltage generation device 810 generates a first voltagefor the first timeframe. After the first voltage has been applied forthe first timeframe, the timer sends a signal to the control circuit 860indicating the first timeframe has elapsed and the control circuit 860directs the switch 870 to move to the second position 872. When theswitch 870 is at the second position 872, the regulated voltage isdirected to a voltage step-down or buck converter 880 to reduce theregulated voltage to a lesser value. The lesser value is then deliveredto the op amp 840 for the second timeframe. After the timer 865 has senta signal to the control circuit 860 that the second timeframe haselapsed, the control circuit 860 moves the switch 870 back to the firstposition. This continues until the desired number of iterations has beencompleted or the stabilization timeframe has elapsed. In an embodimentof the invention, after the sensor stabilization timeframe has elapsed,the sensor transmits a sensor signal 350 to the signal processor 390.

FIG. 8D illustrates a voltage application device 810 utilized to performmore complex applications of voltage to the sensor. The voltageapplication device 810 may include a control device 860, a switch 890, asinusoid voltage generation device 891, a ramp voltage generation device892, and a constant voltage generation device 893. In other embodimentsof the invention, the voltage application may generate an AC wave on topof a DC signal or other various voltage pulse waveforms. In theembodiment of the invention illustrated in FIG. 8D, the control device860 may cause the switch to move to one of the three voltage generationsystems 891 (sinusoid), 892 (ramp), 893 (constant DC). This results ineach of the voltage generation systems generating the identified voltagewaveform. Under certain operating conditions, e.g., where a sinusoidalpulse is to be applied for three pulses, the control device 860 maycause the switch 890 to connect the voltage from the voltage regulator385 to the sinusoid voltage generator 891 in order for the voltageapplication device 810 to generate a sinusoidal voltage. Under otheroperating conditions, e.g., when a ramp voltage is applied to the sensoras the first voltage for a first pulse of three pulses, a sinusoidvoltage is applied to the sensor as the first voltage for a second pulseof the three pulses, and a constant DC voltage is applied to the sensoras the first voltage for a third pulse of the three pulses, the controldevice 860 may cause the switch 890, during the first timeframes in theanodic/cathodic cycles, to move between connecting the voltage from thevoltage generation or application device 810 to the ramp voltagegeneration system 892, then to the sinusoidal voltage generation system891, and then to the constant DC voltage generation system 893. In thisembodiment of the invention, the control device 860 may also bedirecting or controlling the switch to connect certain ones of thevoltage generation subsystems to the voltage from the regulator 385during the second timeframe, e.g., during application of the secondvoltage.

FIG. 9A illustrates a sensor electronics device including amicrocontroller for generating voltage pulses according to an embodimentof the invention. The advanced sensor electronics device may include amicrocontroller 410 (see FIG. 4), a digital-to-analog converter (DAC)420, an op amp 840, and a sensor signal measurement circuit 431. In anembodiment of the invention, the sensor signal measurement circuit maybe a current-to-frequency (I/F) converter 430. In the embodiment of theinvention illustrated in FIG. 9A, software or programmable logic in themicrocontroller 410 provides instructions to transmit signals to the DAC420, which in turn instructs the DAC 420 to output a specific voltage tothe operational amplifier 840. The microcontroller 410 may also beinstructed to output a specific voltage to the working electrode 375, asis illustrated by line 911 in FIG. 9A. As discussed above, theapplication of the specific voltage to operational amplifier 840 and theworking electrode 375 may drive the voltage measured at the counterelectrode to the specific voltage magnitude. In other words, themicrocontroller 410 outputs a signal which is indicative of a voltage ora voltage waveform that is to be applied to the sensor 355 (e.g., theoperational amplifier 840 coupled to the sensor 355). In an alternativeembodiment of the invention, a fixed voltage may be set by applying avoltage directly from the DAC 420 between the reference electrode andthe working electrode 375. A similar result may also be obtained byapplying voltages to each of the electrodes with the difference equal tothe fixed voltage applied between the reference and working electrode.In addition, the fixed voltage may be set by applying a voltage betweenthe reference and the counter electrode. Under certain operatingconditions, the microcontroller 410 may generate a pulse of a specificmagnitude which the DAC 420 understands represents that a voltage of aspecific magnitude is to be applied to the sensor. After a firsttimeframe, the microcontroller 410 (via the program or programmablelogic) outputs a second signal which either instructs the DAC 420 tooutput no voltage (for a sensor electronics device 360 operatingaccording to the method described in FIG. 6A) or to output a secondvoltage (for a sensor electronics device 360 operating according to themethod described in FIG. 6B). The microcontroller 410, after the secondtimeframe has elapsed, then repeats the cycle of sending the signalindicative of a first voltage to be applied (for the first timeframe)and then sending the signal to instruct no voltage is to be applied orthat a second voltage is to be applied (for the second timeframe).

Under other operating conditions, the microcontroller 410 may generate asignal to the DAC 420 which instructs the DAC to output a ramp voltage.Under other operating conditions, the microcontroller 410 may generate asignal to the DAC 420 which instructs the DAC 420 to output a voltagesimulating a sinusoidal voltage. These signals could be incorporatedinto any of the pulsing methodologies discussed above in the precedingparagraph or earlier in the application. In an embodiment of theinvention, the microcontroller 410 may generate a sequence ofinstructions and/or pulses, which the DAC 420 receives and understandsto mean that a certain sequence of pulses is to be applied. For example,the microcontroller 410 may transmit a sequence of instructions (viasignals and/or pulses) that instruct the DAC 420 to generate a constantvoltage for a first iteration of a first timeframe, a ramp voltage for afirst iteration of a second timeframe, a sinusoidal voltage for a seconditeration of a first timeframe, and a squarewave having two values for asecond iteration of the second timeframe.

The microcontroller 410 may include programmable logic or a program tocontinue this cycling for a stabilization timeframe or for a number ofiterations. Illustratively, the microcontroller 410 may include countinglogic to identify when the first timeframe or the second timeframe haselapsed. Additionally, the microcontroller 410 may include countinglogic to identify that a stabilization timeframe has elapsed. After anyof the preceding timeframes have elapsed, the counting logic mayinstruct the microcontroller to either send a new signal or to stoptransmission of a signal to the DAC 420.

The use of the microcontroller 410 allows a variety of voltagemagnitudes to be applied in a number of sequences for a number of timedurations. In an embodiment of the invention, the microcontroller 410may include control logic or a program to instruct the digital-to-analogconverter 420 to transmit a voltage pulse having a magnitude ofapproximately 1.0 volt for a first time period of 1 minute, to thentransmit a voltage pulse having a magnitude of approximately 0.5 voltsfor a second time period of 4 minutes, and to repeat this cycle for fouriterations. In an embodiment of the invention, the microcontroller 420may be programmed to transmit a signal to cause the DAC 420 to apply thesame magnitude voltage pulse for each first voltage in each of theiterations. In an embodiment of the invention, the microcontroller 410may be programmed to transmit a signal to cause the DAC to apply adifferent magnitude voltage pulse for each first voltage in each of theiterations. In this embodiment of the invention, the microcontroller 410may also be programmed to transmit a signal to cause the DAC 420 toapply a different magnitude voltage pulse for each second voltage ineach of the iterations. Illustratively, the microcontroller 410 may beprogrammed to transmit a signal to cause the DAC 420 to apply a firstvoltage pulse of approximately 1.0 volt in the first iteration, to applya second voltage pulse of approximately 0.5 volts in the firstiteration, to apply a first voltage of 0.7 volts and a second voltage of0.4 volts in the second iteration, and to apply a first voltage of 1.2volts and a second voltage of 0.8 volts in the third iteration.

The microcontroller 410 may also be programmed to instruct the DAC 420to provide a number of short duration voltage pulses for a firsttimeframe. In this embodiment of the invention, rather than one voltagebeing applied for the entire first timeframe (e.g., two minutes), anumber of shorter duration pulses may be applied to the sensor. In thisembodiment, the microcontroller 410 may also be programmed to instructthe DAC 420 to provide a number of short duration voltage pulses for thesecond timeframe to the sensor. Illustratively, the microcontroller 410may send a signal to cause the DAC to apply a number of short durationvoltage pulses where the short duration is 50 milliseconds or 100milliseconds. In between these short duration pulses the DAC may applyno voltage or the DAC may apply a minimal voltage. The microcontrollermay cause the DAC 420 to apply the short duration voltage pulses for thefirst timeframe, e.g., two minutes. The microcontroller 410 may thensend a signal to cause the DAC to either not apply any voltage or toapply the short duration voltage pulses at a magnitude of a secondvoltage for a second timeframe to the sensor, e.g., the second voltagemay be 0.75 volts and the second timeframe may be 5 minutes. In anembodiment of the invention, the microcontroller 410 may send a signalto the DAC 420 to cause the DAC 420 to apply a different magnitudevoltage for each of the short duration pulses in the first timeframeand/or in the second timeframe. In an embodiment of the invention, themicrocontroller 410 may send a signal to the DAC 420 to cause the DAC420 to apply a pattern of voltage magnitudes to the short durationsvoltage pulses for the first timeframe or the second timeframe. Forexample, the microcontroller may transmit a signal or pulses instructingthe DAC 420 to apply thirty 20-millisecond pulses to the sensor duringthe first timeframe. Each of the thirty 20-millisecond pulses may havethe same magnitude or may have a different magnitude. In this embodimentof the invention, the microcontroller 410 may instruct the DAC 420 toapply short duration pulses during the second timeframe or may instructthe DAC 420 to apply another voltage waveform during the secondtimeframe.

Although the disclosures in FIGS. 6-8 disclose the application of avoltage, a current may also be applied to the sensor to initiate thestabilization process. Illustratively, in the embodiment of theinvention illustrated in FIG. 6B, a first current may be applied duringa first timeframe to initiate an anodic or cathodic response and asecond current may be applied during a second timeframe to initiate theopposite anodic or cathodic response. The application of the firstcurrent and the second current may continue for a number of iterationsor may continue for a stabilization timeframe. In an embodiment of theinvention, a first current may be applied during a first timeframe and afirst voltage may be applied during a second timeframe. In other words,one of the anodic or cathodic cycles may be triggered by a current beingapplied to the sensor and the other of the anodic or cathodic cycles maybe triggered by a voltage being applied to the sensor. As describedabove, a current applied may be a constant current, a ramp current, astepped pulse current, or a sinusoidal current. Under certain operatingconditions, the current may be applied as a sequence of short durationpulses during the first timeframe.

FIG. 9B illustrates a sensor and sensor electronics utilizing ananalyzation module for feedback in a stabilization period according toan embodiment of the present invention. FIG. 9B introduces ananalyzation module 950 to the sensor electronics device 360. Theanalyzation module 950 utilizes feedback from the sensor to determinewhether or not the sensor is stabilized. In an embodiment of theinvention, the microcontroller 410 may include instructions or commandsto control the DAC 420 so that the DAC 420 applies a voltage or currentto a part of the sensor 355. FIG. 9B illustrates that a voltage orcurrent could be applied between a reference electrode 370 and a workingelectrode 375. However, the voltage or current can be applied in betweenelectrodes or directly to one of the electrodes and the invention shouldnot be limited by the embodiment illustrated in FIG. 9B. The applicationof the voltage or current is illustrated by dotted line 955. Theanalyzation module 950 may measure a voltage, a current, a resistance,or an impedance in the sensor 355. FIG. 9B illustrates that themeasurement occurs at the working electrode 375, but this should notlimit the invention because other embodiments of the invention maymeasure a voltage, a current, a resistance, or an impedance in betweenelectrodes of the sensor or directly at either the reference electrode370 or the counter electrode 365. The analyzation module 950 may receivethe measured voltage, current, resistance, or impedance and may comparethe measurement to a stored value (e.g., a threshold value). Dotted line956 represents the analyzation module 950 reading or taking ameasurement of the voltage, current, resistance, or impedance. Undercertain operating conditions, if the measured voltage, current,resistance, or impedance is above the threshold, the sensor isstabilized and the sensor signal is providing accurate readings of aphysiological condition of a patient. Under other operating conditions,if the measured voltage, current, resistance, or impedance is below thethreshold, the sensor is stabilized. Under other operating conditions,the analyzation module 950 may verify that the measured voltage,current, resistance, or impedance is stable for a specific timeframe,e.g., one minute or two minutes. This may represent that the sensor 355is stabilized and that the sensor signal is transmitting accuratemeasurements of a subject's physiological parameter, e.g., blood glucoselevel. After the analyzation module 950 has determined that the sensoris stabilized and the sensor signal is providing accurate measurements,the analyzation module 950 may transmit a signal (e.g., a sensorstabilization signal) to the microcontroller 410 indicating that thesensor is stabilized and that the microcontroller 410 can start using orreceiving the sensor signal from the sensor 355. This is represented bydotted line 957.

FIG. 10 illustrates a block diagram of a sensor system includinghydration electronics according to an embodiment of the invention. Thesensor system includes a connector 1010, a sensor 1012, and a monitor orsensor electronics device 1025. The sensor 1012 includes electrodes 1020and a connection portion 1024. In an embodiment of the invention, thesensor 1012 may be connected to the sensor electronics device 1025 via aconnector 1010 and a cable. In other embodiments of the invention, thesensor 1012 may be directly connected to the sensor electronics device1025. In other embodiments of the invention, the sensor 1012 may beincorporated into the same physical device as the sensor electronicsdevice 1025. The monitor or sensor electronics device 1025 may include apower supply 1030, a regulator 1035, a signal processor 1040, ameasurement processor 1045, and a processor 1050. The monitor or sensorelectronics device 1025 may also include a hydration detection circuit1060. The hydration detection circuit 1060 interfaces with the sensor1012 to determine if the electrodes 1020 of the sensor 1012 aresufficiently hydrated. If the electrodes 1020 are not sufficientlyhydrated, the electrodes 1020 do not provide accurate glucose readings,so it is important to know when the electrodes 1020 are sufficientlyhydrated. Once the electrodes 1020 are sufficiently hydrated, accurateglucose readings may be obtained.

In an embodiment of the invention illustrated in FIG. 10, the hydrationdetection circuit 1060 may include a delay or timer module 1065 and aconnection detection module 1070. In an embodiment of the inventionutilizing the short term sensor or the subcutaneous sensor, after thesensor 1012 has been inserted into the subcutaneous tissue, the sensorelectronics device or monitor 1025 is connected to the sensor 1012. Theconnection detection module 1070 identifies that the sensors electronicsdevice 1025 has been connected to the sensor 1012 and sends a signal tothe timer module 1065. This is illustrated in FIG. 10 by the arrow 1084which represents a detector 1083 detecting a connection and sending asignal to the connection detection module 1070 indicating the sensor1012 has been connected to the sensor electronics device 1025. In anembodiment of the invention where implantable or long-term sensors areutilized, a connection detection module 1070 identifies that theimplantable sensor has been inserted into the body. The timer module1065 receives the connection signal and waits a set or establishedhydration time. Illustratively, the hydration time may be two minutes,five minutes, ten minutes, or 20 minutes. These examples are meant to beillustrative and not to be limiting. The timeframe does not have to be aset number of minutes and can include any number of seconds. In anembodiment of the invention, after the timer module 1065 has waited forthe set hydration time, the timer module 1065 may notify the processor1050 that the sensor 1012 is hydrated by sending a hydration signal,which is illustrated by line 1086.

In this embodiment of the invention, the processor 1050 may receive thehydration signal and only start utilizing the sensor signal (e.g.,sensor measurements) after the hydration signal has been received. Inanother embodiment of the invention, the hydration detection circuit1060 may be coupled between the sensor (the sensor electrodes 1020) andthe signal processor 1040. In this embodiment of the invention, thehydration detection circuit 1060 may prevent the sensor signal frombeing sent to signal processor 1040 until the timer module 1065 hasnotified the hydration detection circuit 1060 that the set hydrationtime has elapsed. This is illustrated by the dotted lines labeled withreference numerals 1080 and 1081. Illustratively, the timer module 1065may transmit a connection signal to a switch (or transistor) to turn onthe switch and let the sensor signal proceed to the signal processor1040. In an alternative embodiment of the invention, the timer module1065 may transmit a connection signal to turn on a switch 1088 (or closethe switch 1088) in the hydration detection circuit 1060 to allow avoltage from the regulator 1035 to be applied to the sensor 1012 afterthe hydration time has elapsed. In other words, in this embodiment ofthe invention, the voltage from the regulator 1035 is not applied to thesensor 1012 until after the hydration time has elapsed.

FIG. 11 illustrates an embodiment of the invention including amechanical switch to assist in determining a hydration time. In anembodiment of the invention, a single housing may include a sensorassembly 1120 and a sensor electronics device 1125. In an embodiment ofthe invention, the sensor assembly 1120 may be in one housing and thesensor electronics device 1125 may be in a separate housing, but thesensor assembly 1120 and the sensor electronics device 1125 may beconnected together. In this embodiment of the invention, a connectiondetection mechanism 1160 may be a mechanical switch. The mechanicalswitch may detect that the sensor 1120 is physically connected to thesensor electronics device 1125. In an embodiment of the invention, atimer circuit 1135 may also be activated when the mechanical switch 1160detects that the sensor 1120 is connected to the sensor electronicsdevice 1125. In other words, the mechanical switch may close and asignal may be transferred to a timer circuit 1135. Once a hydration timehas elapsed, the timer circuit 1135 transmits a signal to the switch1140 to allow the regulator 1035 to apply a voltage to the sensor 1120.In other words, no voltage is applied until the hydration time haselapsed. In an embodiment of the invention, current may replace voltageas what is being applied to the sensor once the hydration time elapses.In an alternative embodiment of the invention, when the mechanicalswitch 1160 identifies that a sensor 1120 has been physically connectedto the sensor electronics device 1125, power may initially be applied tothe sensor 1120. Power being sent to the sensor 1120 results in a sensorsignal being output from the working electrode in the sensor 1120. Thesensor signal may be measured and sent to a processor 1175. Theprocessor 1175 may include a counter input. Under certain operatingconditions, after a set hydration time has elapsed from when the sensorsignal was input into the processor 1175, the processor 1175 may startprocessing the sensor signal as an accurate measurement of the glucosein a subject's body. In other words, the processor 1170 has received thesensor signal from the potentiostat circuit 1170 for a certain amount oftime, but will not process the signal until receiving an instructionfrom the counter input of the processor identifying that a hydrationtime has elapsed. In an embodiment of the invention, the potentiostatcircuit 1170 may include a current-to-frequency converter 1180. In thisembodiment of the invention, the current-to-frequency converter 1180 mayreceive the sensor signal as a current value and may convert the currentvalue into a frequency value, which is easier for the processor 1175 tohandle.

In an embodiment of the invention, the mechanical switch 1160 may alsonotify the processor 1175 when the sensor 1120 has been disconnectedfrom the sensor electronics device 1125. This is represented by dottedline 1176 in FIG. 11. This may result in the processor 1170 poweringdown or reducing power to a number of components, chips, and/or circuitsof the sensor electronics device 1125. If the sensor 1120 is notconnected, the battery or power source may be drained if the componentsor circuits of the sensor electronics device 1125 are in a power onstate. Accordingly, if the mechanical switch 1160 detects that thesensor 1120 has been disconnected from the sensor electronics device1125, the mechanical switch may indicate this to the processor 1175, andthe processor 1175 may power down or reduce power to one or more of theelectronic circuits, chips, or components of the sensor electronicsdevice 1125.

FIG. 12 illustrates an electrical method of detection of hydrationaccording to an embodiment of the invention. In an embodiment of theinvention, an electrical detecting mechanism for detecting connection ofa sensor may be utilized. In this embodiment of the invention, thehydration detection electronics 1250 may include an AC source 1255 and adetection circuit 1260. The hydration detection electronics 1250 may belocated in the sensor electronics device 1225. The sensor 1220 mayinclude a counter electrode 1221, a reference electrode 1222, and aworking electrode 1223. As illustrated in FIG. 12, the AC source 1255 iscoupled to a voltage setting device 1275, the reference electrode 1222,and the detection circuit 1260. In this embodiment of the invention, anAC signal from the AC source is applied to the reference electrodeconnection, as illustrated by dotted line 1291 in FIG. 12. In anembodiment of the invention, the AC signal is coupled to the sensor 1220through an impedance and the coupled signal is attenuated significantlyif the sensor 1220 is connected to the sensor electronics device 1225.Thus, a low level AC signal is present at an input to the detectioncircuit 1260. This may also be referred to as a highly attenuated signalor a signal with a high level of attenuation. Under certain operatingconditions, the voltage level of the AC signal may beVapplied*(Ccoupling)/(Ccoupling+Csensor). If the detection circuit 1260detects that a high level AC signal (lowly attenuated signal) is presentat an input terminal of the detection circuit 1260, no interrupt is sentto the microcontroller 410 because the sensor 1220 has not beensufficiently hydrated or activated. For example, the input of thedetection circuit 1260 may be a comparator. If the sensor 1220 issufficiently hydrated (or wetted), an effective capacitance formsbetween the counter electrode and the reference electrode (e.g.,capacitance C_(r-c) in FIG. 12), and an effective capacitance formsbetween the reference electrode and the working electrode (e.g.,capacitance C_(w-r) in FIG. 12). In other words, an effectivecapacitance relates to capacitance being formed between two nodes anddoes not represent that an actual capacitor is placed in a circuitbetween the two electrodes. In an embodiment of the invention, the ACsignal from the AC source 1255 is sufficiently attenuated bycapacitances C_(r-c) and C_(w-r) and the detection circuit 1260 detectsthe presence of a low level or highly attenuated AC signal from the ACsource 1255 at the input terminal of the detection circuit 1260. Thisembodiment of the invention is significant because the utilization ofthe existing connections between the sensor 1120 and the sensorelectronics device 1125 reduces the number of connections to the sensor.In other words, the mechanical switch, disclosed in FIG. 11, requires aswitch and associated connections between the sensor 1120 and the sensorelectronics device 1125. It is advantageous to eliminate the mechanicalswitch because the sensor 1120 is continuously shrinking in size and theelimination of components helps achieve this size reduction. Inalternative embodiments of the invention, the AC signal may be appliedto different electrodes (e.g., the counter electrode or the workingelectrode) and the invention may operate in a similar fashion.

As noted above, after the detection circuit 1260 has detected that a lowlevel AC signal is present at the input terminal of the detectioncircuit 1260, the detection circuit 1260 may later detect that a highlevel AC signal, with low attenuation, is present at the input terminal.This represents that the sensor 1220 has been disconnected from thesensor electronics device 1225 or that the sensor is not operatingproperly. If the sensor has been disconnected from the sensorelectronics device 1225, the AC source may be coupled with little or lowattenuation to the input of the detection circuit 1260. As noted above,the detection circuit 1260 may generate an interrupt to themicrocontroller. This interrupt may be received by the microcontrollerand the microcontroller may reduce or eliminate power to one or a numberof components or circuits in the sensor electronics device 1225. Thismay be referred to as the second interrupt. Again, this helps reducepower consumption of the sensor electronics device 1225, specificallywhen the sensor 1220 is not connected to the sensor electronics device1225.

In an alternative embodiment of the invention illustrated in FIG. 12,the AC signal may be applied to the reference electrode 1222, as isillustrated by reference numeral 1291, and an impedance measuring device1277 may measure the impedance of an area in the sensor 1220.Illustratively, the area may be an area between the reference electrodeand the working electrode, as illustrated by dotted line 1292 in FIG.12. Under certain operating conditions, the impedance measuring device1277 may transmit a signal to the detection circuit 1260 if a measuredimpedance has decreased to below an impedance threshold or other setcriteria. This represents that the sensor is sufficiently hydrated.Under other operating conditions, the impedance measuring device 1277may transmit a signal to the detection circuit 1260 once the impedanceis above an impedance threshold. The detection circuit 1260 thentransmits the interrupt to the microcontroller 410. In anotherembodiment of the invention, the impedance measuring device 1277 maytransmit an interrupt or signal directly to the microcontroller.

In an alternative embodiment of the invention, the AC source 1255 may bereplaced by a DC source. If a DC source is utilized, then a resistancemeasuring element may be utilized in place of an impedance measuringelement 1277. In an embodiment of the invention utilizing the resistancemeasuring element, once the resistance drops below a resistancethreshold or a set criteria, the resistance measuring element maytransmit a signal to the detection circuit 1260 (represented by dottedline 1293) or directly to the microcontroller indicating that the sensoris sufficiently hydrated and that power may be applied to the sensor.

In the embodiment of the invention illustrated in FIG. 12, if thedetection circuit 1260 detects a low level or highly attenuated ACsignal from the AC source, an interrupt is generated to themicrocontroller 410. This interrupt indicates that sensor issufficiently hydrated. In this embodiment of the invention, in responseto the interrupt, the microcontroller 410 generates a signal that istransferred to a digital-to-analog converter 420 to instruct or causethe digital-to-analog converter 420 to apply a voltage or current to thesensor 1220. Any of the different sequence of pulses or short durationpulses described above in FIG. 6A, 6B, or 6C or the associated textdescribing the application of pulses, may be applied to the sensor 1220.Illustratively, the voltage from the DAC 420 may be applied to an op-amp1275, the output of which is applied to the counter electrode 1221 ofthe sensor 1220. This results in a sensor signal being generated by thesensor, e.g., the working electrode 1223 of the sensor. Because thesensor is sufficiently hydrated, as identified by the interrupt, thesensor signal created at the working electrode 1223 is accuratelymeasuring glucose. The sensor signal is measured by a sensor signalmeasuring device 431 and the sensor signal measuring device 431transmits the sensor signal to the microcontroller 410 where a parameterof a subject's physiological condition is measured. The generation ofthe interrupt represents that a sensor is sufficiently hydrated and thatthe sensor 1220 is now supplying accurate glucose measurements. In thisembodiment of the invention, the hydration period may depend on the typeand/or the manufacturer of the sensor and on the sensor's reaction toinsertion or implantation in the subject. Illustratively, one sensor1220 may have a hydration time of five minutes and one sensor 1220 mayhave a hydration time of one minute, two minutes, three minutes, sixminutes, or 20 minutes. Again, any amount of time may be an acceptableamount of hydration time for the sensor, but smaller amounts of time arepreferable.

If the sensor 1220 has been connected, but is not sufficiently hydratedor wetted, the effective capacitances C_(r-c) and C_(w-r) may notattenuate the AC signal from the AC source 1255. The electrodes in thesensor 1120 are dry before insertion and because the electrodes are dry,a good electrical path (or conductive path) does not exist between thetwo electrodes. Accordingly, a high level AC signal or lowly attenuatedAC signal may still be detected by the detection circuit 1260 and nointerrupt may be generated. Once the sensor has been inserted, theelectrodes become immersed in the conductive body fluid. This results ina leakage path with lower DC resistance. Also, boundary layer capacitorsform at the metal/fluid interface. In other words, a rather largecapacitance forms between the metal/fluid interface and this largecapacitance looks like two capacitors in series between the electrodesof the sensor. This may be referred to as an effective capacitance. Inpractice, a conductivity of an electrolyte above the electrode is beingmeasured. In some embodiments of the invention, the glucose limitingmembrane (GLM) also illustrates impedance blocking electricalefficiency. An unhydrated GLM results in high impedance, whereas a highmoisture GLM results in low impedance. Low impedance is desired foraccurate sensor measurements.

FIG. 13A illustrates a method of hydrating a sensor according to anembodiment of the present invention. In an embodiment of the invention,the sensor may be physically connected 1310 to the sensor electronicsdevice. After the connection, in one embodiment of the invention, atimer or counter may be initiated to count 1320 a hydration time. Afterthe hydration time has elapsed, a signal may be transmitted 1330 to asubsystem in the sensor electronics device to initiate the applicationof a voltage to the sensor. As discussed above, in an embodiment of theinvention, a microcontroller may receive the signal and instruct the DACto apply a voltage to the sensor or in another embodiment of theinvention, a switch may receive a signal which allows a regulator toapply a voltage to the sensor. The hydration time may be five minutes,two minutes, ten minutes and may vary depending on the subject and alsoon the type of sensor.

In an alternative embodiment of the invention, after the connection ofthe sensor to the sensor electronics device, an AC signal (e.g., a lowvoltage AC signal) may be applied 1340 to the sensor, e.g., thereference electrode of the sensor. The AC signal may be applied becausethe connection of the sensor to the sensor electronics device allows theAC signal to be applied to the sensor. After application of the ACsignal, an effective capacitance forms 1350 between the electrode in thesensor that the voltage is applied to and the other two electrodes. Adetection circuit determines 1360 what level of the AC signal is presentat the input of the detection circuit. If a low level AC signal (orhighly attenuated AC signal) is present at the input of the detectioncircuit, due to the effective capacitance forming a good electricalconduit between the electrodes and the resulting attenuation of the ACsignal, an interrupt is generated 1370 by the detection circuit and sentto a microcontroller.

The microcontroller receives the interrupt generated by the detectioncircuit and transmits 1380 a signal to a digital-to-analog converterinstructing or causing the digital-to-analog converter to apply avoltage to an electrode of the sensor, e.g., the counter electrode. Theapplication of the voltage to the electrode of the sensor results in thesensor creating or generating a sensor signal 1390. A sensor signalmeasurement device 431 measures the generated sensor signal andtransmits the sensor signal to the microcontroller. The microcontrollerreceives 1395 the sensor signal from the sensor signal measurementdevice, which is coupled to the working electrode, and processes thesensor signal to extract a measurement of a physiological characteristicof the subject or patient.

FIG. 13B illustrates an additional method for verifying hydration of asensor according to an embodiment of the present invention. In theembodiment of the invention illustrated in FIG. 13B, the sensor isphysically connected 1310 to the sensor electronics device. In anembodiment of the invention, an AC signal is applied 1341 to anelectrode, e.g., a reference electrode, in the sensor. Alternatively, inan embodiment of the invention, a DC signal is applied 1341 to anelectrode in the sensor. If an AC signal is applied, an impedancemeasuring element measures 1351 an impedance at a point within thesensor. Alternatively, if a DC signal is applied, a resistance measuringelement measures 1351 a resistance at a point within the sensor. If theresistance or impedance is lower than a resistance threshold or animpedance threshold, respectively, (or other set criteria), then theimpedance (or resistance) measuring element transmits 1361 (or allows asignal to be transmitted) to the detection circuit, and the detectioncircuit transmits an interrupt to the microcontroller identifying thatthe sensor is hydrated. The reference numbers 1380, 1390, and 1395 arethe same in FIGS. 13A and 13B because they represent the same action.

The microcontroller receives the interrupt and transmits 1380 a signalto a digital-to-analog converter to apply a voltage to the sensor. In analternative embodiment of the invention, the digital-to-analog convertercan apply a current to the sensor, as discussed above. The sensor, e.g.,the working electrode, creates 1390 a sensor signal, which represents aphysiological parameter of a patient. The microcontroller receives 1395the sensor signal from a sensor signal measuring device, which measuresthe sensor signal at an electrode in the sensor, e.g., the workingelectrode. The microcontroller processes the sensor signal to extract ameasurement of the physiological characteristic of the subject orpatient, e.g., the blood glucose level of the patient.

FIGS. 14A and 14B illustrate methods of combining hydrating of a sensorwith stabilizing of a sensor according to an embodiment of the presentinvention. In an embodiment of the invention illustrated in FIG. 14A,the sensor is connected 1405 to the sensor electronics device. The ACsignal is applied 1410 to an electrode of the sensor. The detectioncircuit determines 1420 what level of the AC signal is present at aninput of the detection circuit. If the detection circuit determines thata low level of the AC signal is present at the input (representing ahigh level of attenuation to the AC signal), an interrupt is sent 1430to microcontroller. Once the interrupt is sent to the microcontroller,the microcontroller knows to begin or initiate 1440 a stabilizationsequence, i.e., the application of a number of voltage pulses to anelectrode of the sensors, as described above. For example, themicrocontroller may cause a digital-to-analog converter to apply threevoltage pulses (having a magnitude of +0.535 volts) to the sensor witheach of the three voltage pulses followed by a period of three voltagepulses (having a magnitude of 1.07 volts to be applied). This may bereferred to transmitting a stabilization sequence of voltages. Themicrocontroller may cause this by the execution of a software program ina read-only memory (ROM) or a random access memory. After thestabilization sequence has finished executing, the sensor may generate1450 a sensor signal, which is measured and transmitted to amicrocontroller.

In an embodiment of the invention, the detection circuit may determine1432 that a high level AC signal has continued to be present at theinput of the detection circuit (e.g., an input of a comparator), evenafter a hydration time threshold has elapsed. For example, the hydrationtime threshold may be 10 minutes. After 10 minutes has elapsed, thedetection circuit may still be detecting that a high level AC signal ispresent. At this point in time, the detection circuit may transmit 1434a hydration assist signal to the microcontroller. If the microcontrollerreceives the hydration assist signal, the microcontroller may transmit1436 a signal to cause a DAC to apply a voltage pulse or a series ofvoltage pulses to assist the sensor in hydration. In an embodiment ofthe invention, the microcontroller may transmit a signal to cause theDAC to apply a portion of the stabilization sequence or other voltagepulses to assist in hydrating the sensor. In this embodiment of theinvention, the application of voltage pulses may result in the low levelAC signal (or highly attenuated signal) being detected 1438 at thedetection circuit. At this point, the detection circuit may transmit aninterrupt, as is disclosed in step 1430, and the microcontroller mayinitiate a stabilization sequence.

FIG. 14B illustrates a second embodiment of a combination of a hydrationmethod and a stabilization method where feedback is utilized in thestabilization process. A sensor is connected 1405 to a sensorelectronics device. An AC signal (or a DC signal) is applied 1411 to thesensor. In an embodiment of the invention, the AC signal (or the DCsignal) is applied to an electrode of the sensor, e.g. the referenceelectrode. An impedance measuring device (or resistance measuringdevice) measures 1416 the impedance (or resistance) within a specifiedarea of the sensor. In an embodiment of the invention, the impedance (orresistance) may be measured between the reference electrode and theworking electrode. The measured impedance (or resistance) may becompared 1421 to an impedance or resistance value to see if theimpedance (or resistance) is low enough in the sensor, which indicatesthe sensor is hydrated. If the impedance (or resistance) is below theimpedance (or resistance) value or other set criteria, (which may be athreshold value), an interrupt is transmitted 1431 to themicrocontroller. After receiving the interrupt, the microcontrollertransmits 1440 a signal to the DAC instructing the DAC to apply astabilization sequence of voltages (or currents) to the sensor. Afterthe stabilization sequence has been applied to the sensor, a sensorsignal is created in the sensor (e.g., at the working electrode), ismeasured by a sensor signal measuring device, is transmitted by thesensor signal measuring device, and is received 1450 by themicrocontroller. Because the sensor is hydrated and the stabilizationsequence of voltages has been applied to the sensor, the sensor signalis accurately measuring a physiological parameter (i.e., blood glucose).

FIG. 14C illustrates a third embodiment of the invention where astabilization method and hydration method are combined. In thisembodiment of the invention, the sensor is connected 1500 to the sensorelectronics device. After the sensor is physically connected to thesensor electronics device, an AC signal (or DC signal) is applied 1510to an electrode (e.g., reference electrode) of the sensor. At the sametime, or around the same time, the microcontroller transmits a signal tocause the DAC to apply 1520 a stabilization voltage sequence to thesensor. In an alternative embodiment of the invention, a stabilizationcurrent sequence may be applied to the sensor instead of a stabilizationvoltage sequence. The detection circuit determines 1530 what level of anAC signal (or DC signal) is present at an input terminal of thedetection circuit. If there is a low level AC signal (or DC signal),representing a highly attenuated AC signal (or DC signal), present atthe input terminal of the detection circuit, an interrupt is transmitted1540 to the microcontroller. Because the microcontroller has alreadyinitiated the stabilization sequence, the microcontroller receives theinterrupt and sets 1550 a first indicator that the sensor issufficiently hydrated. After the stabilization sequence is complete, themicrocontroller sets 1555 a second indicator indicating the completionof the stabilization sequence. The application of the stabilizationsequence voltages results in the sensor, e.g., the working electrode,creating 1560 a sensor signal, which is measured by a sensor signalmeasuring circuit, and sent to the microcontroller. If the secondindicator that the stabilization sequence is complete is set and thefirst indicator that the hydration is complete is set, themicrocontroller is able to utilize 1570 the sensor signal. If one orboth of the indicators are not set, the microcontroller may not utilizethe sensor signal because the sensor signal may not represent accuratemeasurements of the physiological measurements of the subject.

The above-described hydration and stabilization processes may be used,in general, as part of a larger continuous glucose monitoring (CGM)methodology. The current state of the art in continuous glucosemonitoring is largely adjunctive, meaning that the readings provided bya CGM device (including, e.g., an implantable or subcutaneous sensor)cannot be used without a reference value in order to make a clinicaldecision. The reference value, in turn, must be obtained from a fingerstick using, e.g., a BG meter. The reference value is needed becausethere is a limited amount of information that is available from thesensor/sensing component. Specifically, the only pieces of informationthat are currently provided by the sensing component for processing arethe raw sensor value (i.e., the sensor current or Isig) and the countervoltage, which is the voltage between the counter electrode and thereference electrode (see, e.g., FIG. 5). Therefore, during analysis, ifit appears that the raw sensor signal is abnormal (e.g., if the signalis decreasing), the only way one can distinguish between a sensorfailure and a physiological change within the user/patient (i.e.,glucose level changing in the body) is by acquiring a reference glucosevalue via a finger stick. As is known, the reference finger stick isalso used for calibrating the sensor.

Embodiments of the inventions described herein are directed toadvancements and improvements in continuous glucose monitoring resultingin a more autonomous system, as well as related devices andmethodologies, wherein the requirement of reference finger sticks may beminimized, or eliminated, and whereby clinical decisions may be madebased on information derived from the sensor signal alone, with a highlevel of reliability. From a sensor-design standpoint, in accordancewith embodiments of the invention, such autonomy may be achieved throughelectrode redundancy, sensor diagnostics, and Isig and/or sensor glucose(SG) fusion.

As will be explored further hereinbelow, redundancy may be achievedthrough the use of multiple working electrodes (e.g., in addition to acounter electrode and a reference electrode) to produce multiple signalsindicative of the patient's blood glucose (BG) level. The multiplesignals, in turn, may be used to assess the relative health of the(working) electrodes, the overall reliability of the sensor, and thefrequency of the need, if at all, for calibration reference values.

Sensor diagnostics includes the use of additional (diagnostic)information which can provide a real-time insight into the health of thesensor. In this regard, it has been discovered that ElectrochemicalImpedance Spectroscopy (EIS) provides such additional information in theform of sensor impedance and impedance-related parameters at differentfrequencies. Moreover, advantageously, it has been further discoveredthat, for certain ranges of frequencies, impedance and/orimpedance-related data are substantially glucose independent. Suchglucose independence enables the use of a variety of EIS-based markersor indicators for not only producing a robust, highly-reliable sensorglucose value (through fusion methodologies), but also assessing thecondition, health, age, and efficiency of individual electrode(s) and ofthe overall sensor substantially independently of the glucose-dependentIsig.

For example, analysis of the glucose-independent impedance data providesinformation on the efficiency of the sensor with respect to how quicklyit hydrates and is ready for data acquisition using, e.g., values for 1kHz real-impedance, 1 kHz imaginary impedance, and Nyquist Slope (to bedescribed in more detail hereinbelow). Moreover, glucose-independentimpedance data provides information on potential occlusion(s) that mayexist on the sensor membrane surface, which occlusion(s) may temporarilyblock passage of glucose into the sensor and thus cause the signal todip (using, e.g., values for 1 kHz real impedance). In addition,glucose-independent impedance data provides information on loss ofsensor sensitivity during extended wear—potentially due to local oxygendeficit at the insertion site—using, e.g., values for phase angle and/orimaginary impedance at 1 kHz and higher frequencies.

Within the context of electrode redundancy and EIS, as well as othercontexts, as will be described in further detail hereinbelow, a fusionalgorithm may be used to take the diagnostic information provided by EISfor each redundant electrode and assess the reliability of eachelectrode independently. Weights, which are a measure of reliability,may then be added for each independent signal, and a single fused signalmay be calculated that can be used to generate sensor glucose values asseen by the patient/subject.

As can be seen from the above, the combined use of redundancy, sensordiagnostics using EIS, and EIS-based fusion algorithms allows for anoverall CGM system that is more reliable than what is currentlyavailable. Redundancy is advantageous in at least two respects. First,redundancy removes the risk of a single point of failure by providingmultiple signals. Second, providing multiple (working) electrodes wherea single electrode may be sufficient allows the output of the redundantelectrode to be used as a check against the primary electrode, therebyreducing, and perhaps eliminating, the need for frequent calibrations.In addition, EIS diagnostics scrutinize the health of each electrodeautonomously without the need for a reference glucose value (fingerstick), thereby reducing the number of reference values required.However, the use of EIS technology and EIS diagnostic methods is notlimited to redundant systems, i.e., those having more than one workingelectrode. Rather, is discussed below in connection with embodiments ofthe invention, EIS may be advantageously used in connection with single-and/or multiple-electrode sensors.

EIS, or AC impedance methods, study the system response to theapplication of a periodic small amplitude AC signal. This is shownillustratively in FIG. 15A, where E is the applied potential, I is thecurrent, and impedance (Z) is defined as ΔE/ΔI. However, althoughimpedance, per se, may be mathematically simply defined as ΔE/ΔI,heretofore, there has been no commercialization success in applicationof EIS technology to continuous glucose monitoring. This has been due,in part, to the fact that glucose sensors are very complicated systemsand, so far, no mathematical models have been developed which cancompletely explain the complexity of the EIS output for a glucosesensor.

One simplified electrical circuit model that has been used to describeelectrochemical impedance spectroscopy is shown in FIG. 15B. In thisillustration, IHP stands for Inner Helmholtz Plane, OHP stands for OuterHelmholtz Plane, CE is the counter electrode, WE is the workingelectrode, C_(d) is double layer capacitance, R_(p) is polarizationresistance, Z_(w) is Warburg impedance, and R_(s) is solutionresistance. Each of the latter four components—double layer capacitance(C_(d)), Warburg impedance (Z_(w)), polarization resistance (R_(p)), andsolution resistance (R_(s))—may play a significant role in sensorperformance, and can be measured separately by applying low- orhigh-frequency alternating working potential. For example, Warburgimpedance is closely related to diffusional impedance of electrochemicalsystems—which is primarily a low-frequency impedance—and, as such,exists in all diffusion-limited electrochemical sensors. Thus, bycorrelating one or more of these components with one or more componentsand/or layers of a glucose sensor, one may use EIS technology as asensor-diagnostics tool.

As is known, impedance may be defined in terms of its magnitude andphase, where the magnitude (|Z|) is the ratio of the voltage differenceamplitude to the current amplitude, and the phase (θ) is the phase shiftby which the current is ahead of the voltage. When a circuit is drivensolely with direct current (DC), the impedance is the same as theresistant, i.e., resistance is a special case of impedance with zerophase angle. However, as a complex quantity, impedance may also berepresented by its real and imaginary parts. In this regard, the realand imaginary impedance can be derived from the impedance magnitude andphase using the following equations:

Real Impedance(ω)=Magnitude(ω)×cos(Phase(ω)/180×π)

Imaginary Impedance(ω)=Magnitude(ω)×sin(Phase(ω)/180×π)

where ω represents the input frequency at which the magnitude (in ohms)and the phase (in degrees) are measured. The relationship betweenimpedance, on the one hand, and current and voltage on theother—including how the former may be calculated based on measurement ofthe latter—will be explored more fully below in connection with thesensor electronics, including the Application Specific IntegratedCircuit (ASIC), that has been developed for use in embodiments of theinvention.

Continuing with the circuit model shown in FIG. 15B, total systemimpedance may be simplified as:

${Z_{t}(\omega)} = {{Z_{w}(\omega)} + R_{s} + \frac{R_{p}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}} - {j\frac{\omega \; R_{p}^{2}C_{d}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}}}}$

where Z_(w)(ω) is the Warburg impedance, ω is the angular velocity, j isthe imaginary unit (used instead of the traditional “i” so as not to beconfused with electric current), and C_(d), R_(p), and R_(s) are thedouble layer capacitance, the polarization resistance, and the solutionresistance, respectively (as defined previously). Warburg impedance canbe calculated as

${Z_{w}(\omega)} = {Z_{0}\frac{\tanh \left( ({js})^{m} \right)}{({js})^{m}}}$$s = {\frac{L^{2}}{\omega/D} = \left( \frac{{Membrane}\mspace{14mu} {Thickness}}{{Frequency}\mspace{14mu} {Dependent}\mspace{14mu} {Diffusion}\mspace{14mu} {Length}} \right)^{2}}$$Z_{0} = \frac{RTL}{n^{2}F^{2}{DC}}$

where D is diffusivity, L is the sensor membrane thickness, C isPeroxide concentration, and m: ½ corresponds to a 45° Nyquist slope.

A Nyquist plot is a graphical representation, wherein the real part ofimpedance (Real Z) is plotted against its imaginary part (Img Z) acrossa spectrum of frequencies. FIG. 16A shows a generalized example of aNyquist Plot, where the X value is the real part of the impedance andthe Y value is the imaginary part of the impedance. The phase angle isthe angle between the impedance point (X,Y)—which defines a vectorhaving magnitude |Z|—and the X axis.

The Nyquist plot of FIG. 16A is generated by applying AC voltages plus aDC voltage (DC bias) between the working electrode and the counterelectrode at selected frequencies from 0.1 Hz to 1000 MHz (i.e., afrequency sweep). Starting from the right, the frequency increases from0.1 Hz. With each frequency, the real and imaginary impedance can becalculated and plotted. As shown, a typical Nyquist plot of anelectrochemical system may look like a semicircle joined with a straightline at an inflection point, wherein the semicircle and the lineindicate the plotted impedance. In certain embodiments, the impedance atthe inflection point is of particular interest since it is easiest toidentify in the Nyquist plot and may define an intercept. Typically, theinflection point is close to the X axis, and the X value of theinflection point approximates the sum of the polarization resistance andsolution resistance (R_(p)+R_(s)).

With reference to FIG. 16B, a Nyquist plot may typically be described interms of a lower-frequency region 1610 and a higher-frequency region1620, where the labels “higher frequency” and “lower frequency” are usedin a relative sense, and are not meant to be limiting. Thus, forexample, the lower-frequency region 1610 may illustratively include datapoints obtained for a frequency range between about 0.1 Hz and about 100Hz (or higher), and the higher-frequency region 1620 may illustrativelyinclude data points obtained for a frequency range between about 1 kHz(or lower) and about 8 kHz (and higher). In the lower-frequency region1610, the Nyquist slope represents the gradient of the linear fit 1630of the lower-frequency data points in the Nyquist plot. As shown, in thehigher-frequencies region 1620, the value of imaginary impedance isminimal, and may become negligible. As such, the intercept 1600 isessentially the value of the real impedance at the higher frequencies(e.g., approximately in the 1 kHz to 8 kHz range in this case). In FIG.16B, the intercept 1600 is at about 25 kOhms.

FIGS. 16C and 16D demonstrate how a glucose sensor responds to asinusoidal (i.e., alternating) working potential. In these figures, GLMis the sensor's glucose limiting membrane, AP is the adhesion promoter,HSA is human serum albumin, GOX is glucose oxidase enzyme (layer),E_(dc) is DC potential, E_(ac) is AC potential, and C′_(peroxide) isperoxide concentration during AC application. As shown in FIG. 16C, ifthe sensor diffusion length, which is a function of AC potentialfrequency, molecular diffusivity, and membrane thickness, is smallcompared to the membrane (GOX) length, the system gives a relativelylinear response with a constant phase angle (i.e., infinite). Incontrast, if the diffusion length is equal to the membrane (GOX) length,the system response will become finite, resulting in a semi-circleNyquist plot, as shown in FIG. 16D. The latter usually holds true forlow-frequency EIS, where the non-Faradaic process is negligible.

In performing an EIS analysis, an AC voltage of various frequencies anda DC bias may be applied between, e.g., the working and referenceelectrodes. In this regard, EIS is an improvement over previousmethodologies that may have limited the application to a simple DCcurrent or an AC voltage of single frequency. Although, generally, EISmay be performed at frequencies in the μHz to MHz range, in embodimentsof the invention, a narrower range of frequencies (e.g., between about0.1 Hz and about 8 kHz) may be sufficient. Thus, in embodiments of theinvention, AC potentials may be applied that fall within a frequencyrange of between about 0.1 Hz and about 8 kHz, with a programmableamplitude of up to at least 100 mV, and preferably at about 50 mV.

Within the above-mentioned frequency range, the relatively-higherfrequencies—i.e., those that fall generally between about 1 kHz andabout 8 kHz—are used to scrutinize the capacitive nature of the sensor.Depending on the thickness and permeability of membranes, a typicalrange of impedance at the relatively-higher frequencies may be, e.g.,between about 500 Ohms and 25 kOhms, and a typical range for the phasemay be, e.g., between 0 degrees and −40 degrees. The relatively-lowerfrequencies—i.e., those that fall generally between about 0.1 Hz andabout 100 Hz—on the other hand, are used to scrutinize the resistivenature of the sensor. Here, depending on electrode design and the extentof metallization, a typical functioning range for output real impedancemay be, e.g., between about 50 kOhms and 300 kOhms, and a typical rangefor the phase may be between about −50 degrees to about −90 degrees. Theabove illustrative ranges are shown, e.g., in the Bode plots of FIGS.16E and 16F.

As noted previously, the phrases “higher frequencies” and “lowerfrequencies” are meant to be used relative to one another, rather thanin an absolute sense, and they, as well as the typical impedance andphase ranges mentioned above, are meant to be illustrative, and notlimiting. Nevertheless, the underlying principle remains the same: thecapacitive and resistive behavior of a sensor can be scrutinized byanalyzing the impedance data across a frequency spectrum, wherein,typically, the lower frequencies provide information about the moreresistive components (e.g., the electrode, etc.), while the higherfrequencies provide information about the capacitive components (e.g.,membranes). However, the actual frequency range in each case isdependent on the overall design, including, e.g., the type(s) ofelectrode(s), the surface area of the electrode(s), membrane thickness,the permeability of the membrane, and the like. See also FIG. 15Bregarding general correspondence between high-frequency circuitcomponents and the sensor membrane, as well as between low-frequencycircuit components and the Faradaic process, including, e.g., theelectrode(s).

EIS may be used in sensor systems where the sensor includes a singleworking electrode, as well those in which the sensor includes multiple(redundant) working electrodes. In one embodiment, EIS provides valuableinformation regarding the age (or aging) of the sensor. Specifically, atdifferent frequencies, the magnitude and the phase angle of theimpedance vary. As seen in FIG. 17, the sensor impedance—in particular,the sum of Rp and Rs—reflects the sensor age as well as the sensor'soperating conditions. Thus, a new sensor normally has higher impedancethan a used sensor as seen from the different plots in FIG. 17. In thisway, by considering the X-value of the sum of Rp and Rs, a threshold canbe used to determine when the sensor's age has exceeded the specifiedoperating life of the sensor. It is noted that, although for theillustrative examples shown in FIGS. 17-21 and discussed below, thevalue of real impedance at the inflection point (i.e., Rp+Rs) is used todetermine the aging, status, stabilization, and hydration of the sensor,alternative embodiments may use other EIS-based parameters, such as,e.g., imaginary impedance, phase angle, Nyquist slope, etc. in additionto, or in place of, real impedance.

FIG. 17 illustrates an example of a Nyquist plot over the life time of asensor. The points indicated by arrows are the respective inflectionpoints for each of the sweeps across the frequency spectrum. Forexample, before initialization (at time t=0), Rs+Rp is higher than 8.5kOhms, and after initialization (at time t=0.5 hr), the value of Rs+Rpdropped to below 8 kOhms. Over the next six days, Rs+Rp continues todecrease, such that, at the end of the specified sensor life, Rs+Rpdropped to below 6.5 kOhms. Based on such examples, a threshold valuecan be set to specify when the Rs+Rp value would indicate the end of thespecified operating life of the sensor. Therefore, the EIS techniqueallows closure of the loophole of allowing a sensor to be re-used beyondthe specified operating time. In other words, if the patient attempts tore-use a sensor after the sensor has reached its specified operatingtime by disconnecting and then re-connecting the sensor again, the EISwill measure abnormally-low impedance, thereby enabling the system toreject the sensor and prompt the patient for a new sensor.

Additionally, EIS may enable detection of sensor failure by detectingwhen the sensor's impedance drops below a low impedance threshold levelindicating that the sensor may be too worn to operate normally. Thesystem may then terminate the sensor before the specified operatinglife. As will be explored in more detail below, sensor impedance canalso be used to detect other sensor failure (modes). For example, when asensor goes into a low-current state (i.e., sensor failure) due to anyvariety of reasons, the sensor impedance may also increase beyond acertain high impedance threshold. If the impedance becomes abnormallyhigh during sensor operation, due, e.g., to protein or polypeptidefouling, macrophage attachment or any other factor, the system may alsoterminate the sensor before the specified sensor operating life.

FIG. 18 illustrates how the EIS technique can be applied during sensorstabilization and in detecting the age of the sensor in accordance withembodiments of the invention. The logic of FIG. 18 begins at 1800 afterthe hydration procedure and sensor initialization procedure describedpreviously has been completed. In other words, the sensor has beendeemed to be sufficiently hydrated, and the first initializationprocedure has been applied to initialize the sensor. The initializationprocedure may preferably be in the form of voltage pulses as describedpreviously in the detailed description. However, in alternativeembodiments, different waveforms can be used for the initializationprocedure. For example, a sine wave can be used, instead of the pulses,to accelerate the wetting or conditioning of the sensor. In addition, itmay be necessary for some portion of the waveform to be greater than thenormal operating voltage of the sensor, i.e., 0.535 volt.

At block 1810, an EIS procedure is applied and the impedance is comparedto both a first high and a first low threshold. An example of a firsthigh and first low threshold value would be 7 kOhms and 8.5 kOhms,respectively, although the values can be set higher or lower as needed.If the impedance, for example, Rp+Rs, is higher than the first highthreshold, the sensor undergoes an additional initialization procedure(e.g., the application of one or more additional pulses) at block 1820.Ideally, the number of total initialization procedures applied toinitialize the sensor would be optimized to limit the impact on both thebattery life of the sensor and the overall amount of time needed tostabilize a sensor. Thus, by applying EIS, fewer initializations can beinitially performed, and the number of initializations can beincrementally added to give just the right amount of initializations toready the sensor for use. Similarly, in an alternative embodiment, EIScan be applied to the hydration procedure to minimize the number ofinitializations needed to aid the hydration process as described inFIGS. 13-14.

On the other hand, if the impedance, for example, Rp+Rs, is below thefirst low threshold, the sensor will be determined to be faulty andwould be terminated immediately at block 1860. A message will be givento the user to replace the sensor and to begin the hydration processagain. If the impedance is within the high and low thresholds, thesensor will begin to operate normally at block 1830. The logic thenproceeds to block 1840 where an additional EIS is performed to check theage of the sensor. The first time the logic reaches block 1840, themicrocontroller will perform an EIS to gauge the age of the sensor toclose the loophole of the user being able to plug in and plug out thesame sensor. In future iterations of the EIS procedure as the logicreturns to block 1840, the microprocessor will perform an EIS at fixedintervals during the specified life of the sensor. In one preferredembodiment, the fixed interval is set for every 2 hours, however, longeror shorter periods of time can easily be used.

At block 1850, the impedance is compared to a second set of high and lowthresholds. An example of such second high and low threshold values maybe 5.5 kOhms and 8.5 kOhms, respectively, although the values can be sethigher or lower as needed. As long as the impedance values stay within asecond high and low threshold, the logic proceeds to block 1830, wherethe sensor operates normally until the specified sensor life, forexample, 5 days, is reached. Of course, as described with respect toblock 1840, EIS will be performed at the regularly scheduled intervalsthroughout the specified sensor life. However, if, after the EIS isperformed, the impedance is determined to have dropped below a secondlower threshold or risen above a second higher threshold at block 1850,the sensor is terminated at block 1860. In further alternativeembodiments, a secondary check can be implemented of a faulty sensorreading. For example, if the EIS indicates that the impedance is out ofthe range of the second high and low thresholds, the logic can perform asecond EIS to confirm that the second set of thresholds is indeed notmet (and confirm that the first EIS was correctly performed) beforedetermining the end of sensor at block 1860.

FIG. 19 builds upon the above description and details a possibleschedule for performing diagnostic EIS procedures in accordance withpreferred embodiments of the present invention. Each diagnostic EISprocedure is optional and it is possible to not schedule any diagnosticEIS procedure or to have any combination of one or more diagnostic EISprocedures, as deemed needed. The schedule of FIG. 19 begins at sensorinsertion at point 1900. Following sensor insertion, the sensorundergoes a hydration period 1910. This hydration period is importantbecause a sensor that is not sufficiently hydrated may give the userinaccurate readings, as described previously. The first optionaldiagnostic EIS procedure at point 1920 is scheduled during thishydration period 1910 to ensure that the sensor is sufficientlyhydrated. The first diagnostic EIS procedure 1920 measures the sensorimpedance value to determine if the sensor has been sufficientlyhydrated. If the first diagnostic EIS procedure 1920 determinesimpedance is within a set high and low threshold, indicating sufficienthydration, the sensor controller will allow the sensor power-up at point1930. Conversely, if the first diagnostic EIS procedure 1920 determinesimpedance is outside a set high and low threshold, indicatinginsufficient hydration, the sensor hydration period 1910 may beprolonged. After prolonged hydration, once a certain capacitance hasbeen reached between the sensor's electrodes, meaning the sensor issufficiently hydrated, power-up at point 1930 can occur.

A second optional diagnostic EIS procedure 1940 is scheduled aftersensor power-up at point 1930, but before sensor initialization startsat point 1950. Scheduled here, the second diagnostic EIS procedure 1940can detect if a sensor is being re-used prior to the start ofinitialization at 1950. The test to determine if the sensor is beingreused was detailed in the description of FIG. 18. However, unlike theprevious description with respect to FIG. 18, where the aging test isperformed after initialization is completed, the aging test is shown inFIG. 19 as being performed before initialization. It is important toappreciate that the timeline of EIS procedures described in FIG. 19 canbe rearranged without affecting the overall teaching of the application,and that the order of some of the steps can be interchanged. Asexplained previously, the second diagnostic EIS procedure 1940 detects are-used sensor by determining the sensor's impedance value and thencomparing it to a set high and low threshold. If impedance falls outsideof the set threshold, indicating the sensor is being re-used, the sensormay then be rejected and the user prompted to replace it with a newsensor. This prevents the complications that may arise out of re-use ofan old sensor. Conversely, if impedance falls within a set threshold,sensor initialization 1950 can start with the confidence that a newsensor is being used.

A third optional diagnostic EIS procedure 1960 is scheduled afterinitialization starts at point 1950. The third diagnostic EIS procedure1960 tests the sensor's impedance value to determine if the sensor isfully initialized. The third diagnostic EIS procedure 1960 should beperformed at the minimum amount of time needed for any sensor to befully initialized. When performed at this time, sensor life is maximizedby limiting the time a fully initialized sensor goes unused, andover-initialization is averted by confirming full initialization of thesensor before too much initialization occurs. Preventingover-initialization is important because over-initialization results ina suppressed current which can cause inaccurate readings. However,under-initialization is also a problem, so if the third diagnostic EISprocedure 1960 indicates the sensor is under-initialized, an optionalinitialization at point 1970 may be performed in order to fullyinitialize the sensor. Under-initialization is disadvantageous becausean excessive current results that does not relate to the actual glucoseconcentration. Because of the danger of under- and over-initialization,the third diagnostic EIS procedure plays an important role in ensuringthe sensor functions properly when used.

In addition, optional periodic diagnostic EIS procedures 1980 can bescheduled for the time after the sensor is fully initialized. The EISprocedures 1980 can be scheduled at any set interval. As will bediscussed in more detail below, EIS procedures 1980 may also betriggered by other sensor signals, such as an abnormal current or anabnormal counter electrode voltage. Additionally, as few or as many EISprocedures 1980 can be scheduled as desired. In preferred embodiments,the EIS procedure used during the hydration process, sensor life check,initialization process, or the periodic diagnostic tests is the sameprocedure. In alternative embodiments, the EIS procedure can beshortened or lengthened (i.e., fewer or more ranges of frequencieschecked) for the various EIS procedures depending on the need to focuson specific impedance ranges. The periodic diagnostic EIS procedures1980 monitor impedance values to ensure that the sensor is continuing tooperate at an optimal level.

The sensor may not be operating at an optimal level if the sensorcurrent has dropped due to polluting species, sensor age, or acombination of polluting species and sensor age. A sensor that has agedbeyond a certain length is no longer useful, but a sensor that has beenhampered by polluting species can possibly be repaired. Pollutingspecies can reduce the surface area of the electrode or the diffusionpathways of analytes and reaction byproducts, thereby causing the sensorcurrent to drop. These polluting species are charged and graduallygather on the electrode or membrane surface under a certain voltage.Previously, polluting species would destroy the usefulness of a sensor.Now, if periodic diagnostic EIS procedures 1980 detect impedance valueswhich indicate the presence of polluting species, remedial action can betaken. When remedial action is to be taken is described with respect toFIG. 20. Periodic diagnostic EIS procedures 1980 therefore becomeextremely useful because they can trigger sensor remedial action whichcan possibly restore the sensor current to a normal level and prolongthe life of the sensor. Two possible embodiments of sensor remedialactions are described below in the descriptions of FIGS. 21A and 21B.

Additionally, any scheduled diagnostic EIS procedure 1980 may besuspended or rescheduled when certain events are determined imminent.Such events may include any circumstance requiring the patient to checkthe sensor reading, including for example when a patient measures his orher BG level using a test strip meter in order to calibrate the sensor,when a patient is alerted to a calibration error and the need to measurehis or her BG level using a test strip meter a second time, or when ahyperglycemic or hypoglycemic alert has been issued but notacknowledged.

FIG. 20 illustrates a method of combining diagnostic EIS procedures withsensor remedial action in accordance with embodiments of the presentinvention. The block 2000 diagnostic procedure may be any of theperiodic diagnostic EIS procedures 1980 as detailed in FIG. 19. Thelogic of this method begins when a diagnostic EIS procedure is performedat block 2000 in order to detect the sensor's impedance value. As noted,in specific embodiments, the EIS procedure applies a combination of a DCbias and an AC voltage of varying frequencies wherein the impedancedetected by performing the EIS procedure is mapped on a Nyquist plot,and an inflection point in the Nyquist plot approximates a sum ofpolarization resistance and solution resistance (i.e., the realimpedance value). After the block 2000 diagnostic EIS procedure detectsthe sensor's impedance value, the logic moves to block 2010.

At block 2010, the impedance value is compared to a set high and lowthreshold to determine if it is normal. If impedance is within the setboundaries of the high and low thresholds at block 2010, normal sensoroperation is resumed at block 2020 and the logic of FIG. 20 will enduntil a time when another diagnostic EIS procedure is scheduled.Conversely, if impedance is determined to be abnormal (i.e., outside theset boundaries of the high and low thresholds) at block 2010, remedialaction at block 2030 is triggered. An example of a high and lowthreshold value that would be acceptable during a sensor life would be5.5 kOhms and 8.5 kOhms, respectively, although the values can be sethigher or lower as needed.

The block 2030 remedial action is performed to remove any of thepolluting species, which may have caused the abnormal impedance value.In preferred embodiments, the remedial action is performed by applying areverse current, or a reverse voltage between the working electrode andthe reference electrode. The specifics of the remedial action will bedescribed in more detail with respect to FIG. 21. After the remedialaction is performed at block 2030, impedance value is again tested by adiagnostic EIS procedure at block 2040. The success of the remedialaction is then determined at block 2050 when the impedance value fromthe block 2040 diagnostic EIS procedure is compared to the set high orlow threshold. As in block 2010, if impedance is within the setthresholds, it is deemed normal, and if impedance is outside the setthresholds, it is deemed abnormal.

If the sensor's impedance value is determined to have been restored tonormal at block 2050, normal sensor operation at block 2020 will occur.If impedance is still not normal, indicating that either sensor age isthe cause of the abnormal impedance or the remedial action wasunsuccessful in removing the polluting species, the sensor is thenterminated at block 2060. In alternative embodiments, instead ofimmediately terminating the sensor, the sensor may generate a sensormessage initially requesting the user to wait and then perform furtherremedial action after a set period of time has elapsed. This alternativestep may be coupled with a separate logic to determine if the impedancevalues are getting closer to being within the boundary of the high andlow threshold after the initial remedial action is performed. Forexample, if no change is found in the sensor impedance values, thesensor may then decide to terminate. However, if the sensor impedancevalues are getting closer to the preset boundary, yet still outside theboundary after the initial remedial action, an additional remedialaction could be performed. In yet another alternative embodiment, thesensor may generate a message requesting the user to calibrate thesensor by taking a finger stick meter measurement to further confirmwhether the sensor is truly failing. All of the above embodiments workto prevent a user from using a faulty sensor that produces inaccuratereadings.

FIG. 21A illustrates one embodiment of the sensor remedial actionpreviously mentioned. In this embodiment, blockage created by pollutingspecies is removed by reversing the voltage being applied to the sensorbetween the working electrode and the reference electrode. The reversedDC voltage lifts the charged, polluting species from the electrode ormembrane surface, clearing diffusion pathways. With cleared pathways,the sensor's current returns to a normal level and the sensor can giveaccurate readings. Thus, the remedial action saves the user the time andmoney associated with replacing an otherwise effective sensor.

FIG. 21B illustrates an alternative embodiment of the sensor remedialaction previously mentioned. In this embodiment, the reversed DC voltageapplied between the working electrode and the reference electrode iscoupled with an AC voltage. By adding the AC voltage, certain tightlyabsorbed species or species on the superficial layer can be removedsince the AC voltage can extend its force further from the electrode andpenetrate all layers of the sensor. The AC voltage can come in anynumber of different waveforms. Some examples of waveforms that could beused include square waves, triangular waves, sine waves, or pulses. Aswith the previous embodiment, once polluting species are cleared, thesensor can return to normal operation, and both sensor life and accuracyare improved.

While the above examples illustrate the use, primarily, of realimpedance data in sensor diagnostics, embodiments of the invention arealso directed to the use of other EIS-based, and substantiallyanalyte-independent, parameters (in addition to real impedance) insensor diagnostic procedures. For example, as mentioned previously,analysis of (substantially) glucose-independent impedance data, such as,e.g., values for 1 kHz real-impedance and 1 kHz imaginary impedance, aswell as Nyquist slope, provide information on the efficiency of thesensor with respect to how quickly it hydrates and is ready for dataacquisition. Moreover, (substantially) glucose-independent impedancedata, such as, e.g., values for 1 kHz real impedance, providesinformation on potential occlusion(s) that may exist on the sensormembrane surface, which occlusion(s) may temporarily block passage ofglucose into the sensor and thus cause the signal to dip.

In addition, (substantially) glucose-independent impedance data, suchas, e.g., values for higher-frequency phase angle and/or imaginaryimpedance at 1 kHz and higher frequencies, provides information on lossof sensor sensitivity during extended wear, which sensitivity loss maypotentially be due to local oxygen deficit at the insertion site. Inthis regard, the underlying mechanism for oxygen deficiency-ledsensitivity loss may be described as follows: when local oxygen isdeficient, sensor output (i.e., Isig and SG) will be dependent on oxygenrather than glucose and, as such, the sensor will lose sensitivity toglucose. Other markers, including 0.1 Hz real impedance, the counterelectrode voltage (Vcntr), and EIS-induced spikes in the Isig may alsobe used for the detection of oxygen deficiency-led sensitivity loss.Moreover, in a redundant sensor system, the relative differences in 1kHz real impedance, 1 kHz imaginary impedance, and 0.1 Hz real impedancebetween two or more working electrodes may be used for the detection ofsensitivity loss due to biofouling.

In accordance with embodiments of the invention, EIS-based sensordiagnostics entails consideration and analysis of EIS data relating toone or more of at least three primary factors, i.e., potential sensorfailure modes: (1) signal start-up; (2) signal dip; and (3) sensitivityloss. Significantly, the discovery herein that a majority of theimpedance-related parameters that are used in such diagnostic analysesand procedures can be studied at a frequency, or within a range offrequencies, where the parameter is substantially analyte-independentallows for implementation of sensor-diagnostic procedures independentlyof the level of the analyte in a patient's body. Thus, while EIS-basedsensor diagnostics may be triggered by, e.g., large fluctuations inIsig, which is analyte-dependent, the impedance-related parameters thatare used in such sensor diagnostic procedures are themselvessubstantially independent of the level of the analyte. As will beexplored in more detail below, it has also been found that, in amajority of situations where glucose may be seen to have an effect onthe magnitude (or other characteristic) of an EIS-based parameter, sucheffect is usually small enough—e.g., at least an order of magnitudedifference between the EIS-based measurement and the glucose effectthereon—such that it can be filtered out of the measurement, e.g., viasoftware in the IC.

By definition, “start-up” refers to the integrity of the sensor signalduring the first few hours (e.g., t=0-6 hours) after insertion. Forexample, in current devices, the signal during the first 2 hours afterinsertion is deemed to be unreliable and, as such, the sensor glucosevalues are blinded to the patient/user. In situations where the sensortakes an extended amount of time to hydrate, the sensor signal is lowfor several hours after insertion. With the use of EIS, additionalimpedance information is available (by running an EIS procedure) rightafter the sensor has been inserted. In this regard, the total impedanceequation may be used to explain the principle behind low-startupdetection using 1 kHz real impedance. At relatively higherfrequencies—in this case, 1 kHz and above—imaginary impedance is verysmall (as confirmed with in-vivo data), such that total impedancereduces to:

${Z_{t}(\omega)} = {R_{s} + \frac{R_{p}}{1 + {\omega^{2}R_{p}^{2}C_{d}^{2}}}}$

As sensor wetting is gradually completed, the double layer capacitance(C_(d)) increases. As a result, the total impedance will decreasebecause, as indicated in the equation above, total impedance isinversely proportional to C_(d). This is illustrated in the form of theintercept 1600 on the real impedance axis shown, e.g., in FIG. 16B.Importantly, the 1 kHz imaginary impedance can also be used for the samepurpose, as it also includes, and is inversely proportional to, acapacitance component.

Another marker for low startup detection is Nyquist slope, which reliessolely on the relatively lower-frequency impedance which, in turn,corresponds to the Warburg impedance component of total impedance (see,e.g., FIG. 15B). FIG. 22 shows a Nyquist plot for a normally-functioningsensor, where Arrow A is indicative of the progression of time, i.e.,sensor wear time, starting from t=0. Thus, EIS at the relatively-lowerfrequencies is performed right after sensor insertion (time t=0), whichgenerates real and imaginary impedance data that is plotted with a firstlinear fit 2200 having a first (Nyquist) slope. At a time interval aftert=0, a second (lower) frequency sweep is run that produces a secondlinear fit 2210 having a second (Nyquist) slope larger than the firstNyquist slope, and so on. As the sensor becomes more hydrated, theNyquist slope increases, and the intercept decrease, as reflected by thelines 2200, 2210, etc. becoming steeper and moving closer to the Y-axis.In connection with low startup detection, clinical data indicates thatthere is typically a dramatic increase of Nyquist slope after sensorinsertion and initialization, which is then stabilized to a certainlevel. One explanation for this is that, as the sensor is graduallywetted, the species diffusivity as well as concentration undergodramatic change, which is reflected in Warburg impedance.

In FIG. 23A, the Isig 2230 for a first working electrode WE1 starts offlower than expected (at about 10 nA), and takes some time to catch upwith the Isig 2240 for a second working electrode WE2. Thus, in thisparticular example, WE1 is designated as having a low start-up. The EISdata reflects this low start-up in two ways. First, as shown in FIG.23A, the real impedance at 1 kHz (2235) of WE1 is much higher than the 1kHz real impedance 2245 of WE2. Second, when compared to the Nyquistslope for WE2 (FIG. 23C), the Nyquist slope for WE1 (FIG. 23B) startsout lower, has a larger intercept 2237, and takes more time tostabilize. As will be discussed later, these two signatures—the 1 kHzreal impedance and the Nyquist slope—can be used as diagnostic inputs ina fusion algorithm to decide which of the two electrodes can carry ahigher weight when the fused signal is calculated. In addition, one orboth of these markers may be used in a diagnostic procedure to determinewhether the sensor, as a whole, is acceptable, or whether it should beterminated and replaced.

By definition, signal (or Isig) dips refer to instances of low sensorsignal, which are mostly temporary in nature, e.g., on the order of afew hours. Such low signals may be caused, for example, by some form ofbiological occlusion on the sensor surface, or by pressure applied atthe insertion site (e.g., while sleeping on the side). During thisperiod, the sensor data is deemed to be unreliable; however, the signaldoes recover eventually. In the EIS data, this type of signal dip—asopposed to one that is caused by a glycemic change in the patient'sbody—is reflected in the 1 kHz real impedance data, as shown in FIG. 24.

Specifically, in FIG. 24, both the Isig 2250 for the first workingelectrode WE1 and the Isig 2260 for the second working electrode WE2start out at about 25 nA at the far left end (i.e., at 6 pm). As timeprogresses, both Isigs fluctuate, which is reflective of glucosefluctuations in the vicinity of the sensor. For about the first 12 hoursor so (i.e., until about 6 am), both Isigs are fairly stable, as aretheir respective 1 kHz real impedances 2255, 2265. However, betweenabout 12 and 18 hours—i.e., between 6 am and noon—the Isig 2260 for WE2starts to dip, and continues a downward trend for the next severalhours, until about 9 pm. During this period, the Isig 2250 for WE1 alsoexhibits some dipping, but Isig 2250 is much more stable, and dips quitea bit less, than Isig 2260 for WE2. The behavior of the Isigs for WE1and WE2 is also reflected in their respective 1 kHz real impedance data.Thus, as shown in FIG. 24, during the time period noted above, while the1 kHz real impedance for WE1 (2255) remains fairly stable, there is amarked increase in the 1 kHz real impedance for WE2 (2265).

By definition, sensitivity loss refers to instances where the sensorsignal (Isig) becomes low and non-responsive for an extended period oftime, and is usually unrecoverable. Sensitivity loss may occur for avariety of reasons. For example, electrode poisoning drastically reducesthe active surface area of the working electrode, thereby severelylimiting current amplitude. Sensitivity loss may also occur due tohypoxia, or oxygen deficit, at the insertion site. In addition,sensitivity loss my occur due to certain forms of extreme surfaceocclusion (i.e., a more permanent form of the signal dip caused bybiological or other factors) that limit the passage of both glucose andoxygen through the sensor membrane, thereby lowering thenumber/frequency of the chemical reactions that generate current in theelectrode and, ultimately, the sensor signal (Isig). It is noted thatthe various causes of sensitivity loss mentioned above apply to bothshort-term (7-10 day wear) and long term (6 month wear) sensors.

In the EIS data, sensitivity loss is often preceded by an increase inthe absolute value of phase (|phase|) and of the imaginary impedance(|imaginary impedance|) at the relatively higher frequency ranges (e.g.,128 Hz and above, and 1 kHz and above, respectively). FIG. 25A shows anexample of a normally-functioning glucose sensor where the sensorcurrent 2500 is responsive to glucose—i.e., Isig 2500 tracks glucosefluctuations—but all relevant impedance outputs, such as, e.g., 1 kHzreal impedance 2510, 1 kHz imaginary impedance 2530, and phase forfrequencies at or above about 128 Hz (2520), remain steady, as they aresubstantially glucose-independent.

Specifically, the top graph in FIG. 25A shows that, after the first fewhours, the 1 kHz real impedance 2510 holds fairly steady at about 5kOhms (and the 1 kHz imaginary impedance 2530 holds fairly steady atabout −400 Ohms). In other words, at 1 kHz, the real impedance data 2510and the imaginary impedance data 2530 are substantiallyglucose-independent, such that they can be used as signatures for, orindependent indicators of, the health, condition, and ultimately,reliability of the specific sensor under analysis. However, as mentionedpreviously, different impedance-related parameters may exhibitglucose-independence at different frequency ranges, and the range, ineach case, may depend on the overall sensor design, e.g., electrodetype, surface area of electrode, thickness of membrane, permeability ofmembrane, etc.

Thus, in the example FIG. 25B—for a 90% short tubeless electrodedesign—the top graph again shows that sensor current 2501 is responsiveto glucose, and that, after the first few hours, the 1 kHz realimpedance 2511 holds fairly steady at about 7.5 kOhms. The bottom graphin FIG. 25B shows real impedance data for frequencies between 0.1 Hz(2518) and 1 kHz (2511). As can be seen, the real impedance data at 0.1Hz (2518) is quite glucose-dependent. However, as indicated by referencenumerals 2516, 2514, and 2512, real impedance becomes more and moreglucose-independent as the frequency increases from 0.1 Hz to 1 kHz,i.e., for impedance data measured at frequencies closer to 1 kHz.

Returning to FIG. 25A, the middle graph shows that the phase 2520 at therelatively-higher frequencies is substantially glucose-independent. Itis noted, however, that “relatively-higher frequencies” in connectionwith this parameter (phase) for the sensor under analysis meansfrequencies of 128 Hz and above. In this regard, the graph shows thatthe phase for all frequencies between 128 Hz and 8 kHz is stablethroughout the period shown. On the other hand, as can be seen in thebottom graph of FIG. 25C, while the phase 2522 at 128 Hz (and above) isstable, the phase 2524 fluctuates—i.e., it becomes more and moreglucose-dependent, and to varying degrees—at frequencies that areincreasingly smaller than 128 Hz. It is noted that the electrode designfor the example of FIG. 25C is the same as that used in FIG. 25B, andthat the top graph in the former is identical to the top graph in thelatter.

FIG. 26 shows an example of sensitivity loss due to oxygen deficiency atthe insertion site. In this case, the insertion site becomes oxygendeprived just after day 4 (designated by dark vertical line in FIG. 26),causing the sensor current 2600 to become low and non-responsive. The 1kHz real impedance 2610 remains stable, indicating no physical occlusionon the sensor. However, as shown by the respective downward arrows,changes in the relatively higher-frequency phase 2622 and 1 kHzimaginary impedance 2632 coincide with loss in sensitivity, indicatingthat this type of loss is due to an oxygen deficit at the insertionsite. Specifically, FIG. 26 shows that the phase at higher frequencies(2620) and the 1 kHz imaginary impedance (2630) become more negativeprior to the sensor losing sensitivity—indicated by the dark verticalline—and continue their downward trend as the sensor sensitivity losscontinues. Thus, as noted above, this sensitivity loss is preceded, orpredicted, by an increase in the absolute value of phase (|phase|) andof the imaginary impedance (|imaginary impedance|) at the relativelyhigher frequency ranges (e.g., 128 Hz and above, and 1 kHz and above,respectively).

The above-described signatures may be verified by in-vitro testing, anexample of which is shown in FIG. 27. FIG. 27 shows the results ofin-vitro testing of a sensor, where oxygen deficit at different glucoseconcentrations is simulated. In the top graph, the Isig fluctuates withthe glucose concentration as the latter is increased from 100 mg/dl(2710) to 200 mg/dl (2720), 300 mg/dl (2730), and 400 mg/dl (2740), andthen decreased back down to 200 and/dl (2750). In the bottom graph, thephase at the relatively-higher frequencies is generally stable,indicating that it is glucose-independent. However, at very low oxygenconcentrations, such as, e.g., at 0.1% O₂, the relatively high-frequencyphase fluctuates, as indicated by the encircled areas and arrows 2760,2770. It is noted that the magnitude and/or direction (i.e., positive ornegative) of fluctuation depend on various factors. For example, thehigher the ratio of glucose concentration to oxygen concentration, thehigher the magnitude of the fluctuation in phase. In addition, thespecific sensor design, as well as the age of the sensor (i.e., asmeasured by time after implant), affect such fluctuations. Thus, e.g.,the older a sensor is, the more susceptible it is to perturbations.

FIGS. 28A-28D show another example of oxygen deficiency-led sensitivityloss with redundant working electrodes WE1 and WE2. As shown in FIG.28A, the 1 kHz real impedance 2810 is steady, even as sensor current2800 fluctuates and eventually becomes non-responsive. Also, as before,the change in 1 kHz imaginary impedance 2820 coincides with the sensor'sloss of sensitivity. In addition, however, FIG. 28B shows real impedancedata and imaginary impedance data (2830 and 2840, respectively) at 0.105Hz. The latter, which may be more commonly referred to as “0.1 kHzdata”, indicates that, whereas imaginary impedance at 0.1 kHz appears tobe fairly steady, 0.1 kHz real impedance 2830 increases considerably asthe sensor loses sensitivity. Moreover, as shown in FIG. 28C, with lossof sensitivity due to oxygen deficiency, V_(cntr) 2850 rails to 1.2Volts.

In short, the diagrams illustrate the discovery that oxygendeficiency-led sensitivity loss is coupled with lower 1 kHz imaginaryimpedance (i.e., the latter becomes more negative), higher 0.105 Hz realimpedance (i.e., the latter becomes more positive), and V_(cntr) rail.Moreover, the oxygen-deficiency process and V_(cntr)-rail are oftencoupled with the increase of the capacitive component in theelectrochemical circuit. It is noted that, in some of the diagnosticprocedures to be described later, the 0.105 Hz real impedance may not beused, as it appears that this relatively lower-frequency real impedancedata may be analyte-dependent.

Finally, in connection with the example of FIGS. 28A-28D, it is notedthat 1 kHz or higher-frequency impedance measurement typically causesEIS-induced spikes in the Isig. This is shown in FIG. 28D, where the rawIsig for WE2 is plotted against time. The drastic increase of Isig whenthe spike starts is a non-Faradaic process, due to double-layercapacitance charge. Thus, oxygen deficiency-led sensitivity loss mayalso be coupled with higher EIS-induced spikes, in addition to lower 1kHz imaginary impedance, higher 0.105 Hz real impedance, and V_(cntr)rail, as discussed above.

FIG. 29 illustrates another example of sensitivity loss. This case maybe thought of as an extreme version of the Isig dip described above inconnection with FIG. 24. Here, the sensor current 2910 is observed to below from the time of insertion, indicating that there was an issue withan insertion procedure resulting in electrode occlusion. The 1 kHzreal-impedance 2920 is significantly higher, while the relativelyhigher-frequency phase 2930 and the 1 kHz imaginary impedance 2940 areboth shifted to much more negative values, as compared to the sameparameter values for the normally-functioning sensor shown in FIG. 25A.The shift in the relatively higher-frequency phase 2930 and 1 kHzimaginary impedance 2940 indicates that the sensitivity loss may be dueto an oxygen deficit which, in turn, may have been caused by anocclusion on the sensor surface.

FIGS. 30A-30D show data for another redundant sensor, where the relativedifferences in 1 kHz real impedance and 1 kHz imaginary impedance, aswell as 0.1 Hz real impedance, between two or more working electrodesmay be used for the detection of sensitivity loss due to biofouling. Inthis example, WE1 exhibits more sensitivity loss than WE2, as is evidentfrom the higher 1 kHz real impedance 3010, lower 1 kHz imaginaryimpedance 3020, and much higher real impedance at 0.105 kHz (3030) forWE2. In addition, however, in this example, V_(cntr) 3050 does not rail.Moreover, as shown in FIG. 30D, the height of the spikes in the raw Isigdata does not change much as time progresses. This indicates that, forsensitivity loss due to biofouling, V_(cntr) rail and the increase inspike height are correlated. In addition, the fact that the height ofthe spikes in the raw Isig data does not change much with time indicatesthat the capacitive component of the circuit does not changesignificantly with time, such that sensitivity loss due to biofouling isrelated to the resistance component of the circuit (i.e., diffusion).

Various of the above-described impedance-related parameters may be used,either individually or in combination, as inputs into: (1) EIS-basedsensor diagnostic procedures; and/or (2) fusion algorithms forgenerating more reliable sensor glucose values. With regard to theformer, FIG. 31 illustrates how EIS-based data—i.e., impedance-relatedparameters, or characteristics—may be used in a diagnostic procedure todetermine, in real time, whether a sensor is behaving normally, orwhether it should be replaced.

The diagnostic procedure illustrated in the flow diagram of FIG. 31 isbased on the collection of EIS data on a periodic basis, such as, e.g.,hourly, every half hour, every 10 minutes, or at any otherinterval—including continuously—as may be appropriate for the specificsensor under analysis. At each such interval, EIS may be run for anentire frequency spectrum (i.e., a “full sweep”), or it may be run for aselected frequency range, or even at a single frequency. Thus, forexample, for an hourly data collection scheme, EIS may be performed atfrequencies in the μHz to MHz range, or it may be run for a narrowerrange of frequencies, such as, e.g., between about 0.1 Hz and about 8kHz, as discussed hereinabove. In embodiments of the invention, EIS dataacquisition may be implemented alternatingly between a full sweep and annarrower-range spectrum, or in accordance with other schemes.

The temporal frequency of EIS implementation and data collection may bedictated by various factors. For example, each implementation of EISconsumes a certain amount of power, which is typically provided by thesensor's battery, i.e., the battery running the sensor electronics,including the ASIC which is described later. As such, battery capacity,as well as the remaining sensor life, may help determine the number oftimes EIS is run, as well as the breadth of frequencies sampled for eachsuch run. In addition, embodiments of the invention envision situationsthat may require that an EIS parameter at a specific frequency (e.g.,real impedance at 1 kHz) be monitored based on a first schedule (e.g.,once every few seconds, or minutes), while other parameters, and/or thesame parameter at other frequencies, can be monitored based on a secondschedule (e.g., less frequently). In these situations, the diagnosticprocedure can be tailored to the specific sensor and requirements, suchthat battery power may be preserved, and unnecessary and/or redundantEIS data acquisition may be avoided.

It is noted that, in embodiments of the invention, a diagnosticprocedure, such as the one shown in FIG. 31, entails a series ofseparate “tests” which are implemented in order to perform real-timemonitoring of the sensor. The multiple tests, or markers—also referredto as “multi markers”—are implemented because each time EIS is run(i.e., each time an EIS procedure is performed), data may be gatheredabout a multiplicity of impedance-based parameters, or characteristics,which can be used to detect sensor condition or quality, including,e.g., whether the sensor has failed or is failing. In performing sensordiagnostics, sometimes, there can be a diagnostic test that may indicatea failure, whereas other diagnostic(s) may indicate no failure.Therefore, the availability of multiple impedance-related parameters,and the implementation of a multi-test procedure, are advantageous, assome of the multiplicity of tests may act as validity checks againstsome of the other tests. Thus, real-time monitoring using a multi-markerprocedure may include a certain degree of built-in redundancy.

With the above in mind, the logic of the diagnostic procedure shown inFIG. 31 begins at 3100, after the sensor has been inserted/implanted,and an EIS run has been made, so as to provide the EIS data as input. At3100, using the EIS data as input, it is first determined whether thesensor is still in place. Thus, if the |Z| slope is found to be constantacross the tested frequency band (or range), and/or the phase angle isabout −90°, it is determined that the sensor is no longer in place, andan alert is sent, e.g., to the patient/user, indicating that sensorpullout has occurred. The specific parameters (and their respectivevalues) described herein for detecting sensor pullout are based on thediscovery that, once the sensor is out of the body and the membrane isno longer hydrated, the impedance spectrum response appears just like acapacitor.

If it is determined that the sensor is still in place, the logic movesto step 3110 to determine whether the sensor is properly initialized. Asshown, the “Init. Check” is performed by determining: (i) whether|(Z_(n)−Z₁)/Z₁|>30% at 1 kHz, where Z₁ is the real impedance measured ata first time, and Z_(n) is the measured impedance at the next interval,at discussed above; and (2) whether the phase angle change is greaterthan 10° at 0.1 Hz. If the answer to either one of the questions is“yes”, then the test is satisfactory, i.e., the Test 1 is not failed.Otherwise, the Test 1 is marked as a failure.

At step 3120, Test 2 asks whether, at a phase angle of −45°, thedifference in frequency between two consecutive EIS runs (f₂−f₁) isgreater than 10 Hz. Again, a “No” answer is marked as a fail; otherwise,Test 2 is satisfactorily met.

Test 3 at step 3130 is a hydration test. Here, the inquiry is whetherthe current impedance Z_(n) is less than the post-initializationimpedance Z_(pi) at 1 kHz. If it is, then this test is satisfied;otherwise, Test 3 is marked as a fail. Test 4 at step 3140 is also ahydration test, but this time at a lower frequency. Thus, this test askswhether Z_(n) is less than 300 kOhms at 0.1 Hz duringpost-initialization sensor operation. Again, a “No” answer indicatesthat the sensor has failed Test 4.

At step 3150, Test 5 inquires whether the low-frequency Nyquist slope isglobally increasing from 0.1 Hz to 1 Hz. As discussed previously, for anormally-operating sensor, the relatively lower-frequency Nyquist slopeshould be increasing over time. Thus, this test is satisfied if theanswer to the inquiry is “yes”; otherwise, the test is marked as failed.

Step 3160 is the last test for this embodiment of the diagnosticprocedure. Here, the inquiry is whether real impedance is globallydecreasing. Again, as was discussed previously, in a normally-operatingsensor, it is expected that, as time goes by, the real impedance shouldbe decreasing. Therefore, a “Yes” answer here would mean that the sensoris operating normally; otherwise, the sensor fails Test 6.

Once all 6 tests have been implemented, a decision is made at 3170 as towhether the sensor is operating normally, or whether it has failed. Inthis embodiment, a sensor is determined to be functioning normally(3172) if it passes at least 3 out of the 6 tests. Put another way, inorder to be determined to have failed (3174), the sensor must fail atleast 4 out of the 6 tests. In alternative embodiments, a different rulemay be used to assess normal operation versus sensor failure. Inaddition, in embodiments of the invention, each of the tests may beweighted, such that the assigned weight reflects, e.g., the importanceof that test, or of the specific parameter(s) queried for that test, indetermining overall sensor operation (normal vs. failed). For example,one test may be weighted twice as heavily as another, but only half asheavily as a third test, etc.

In other alternative embodiments, a different number of tests and/or adifferent set of EIS-based parameters for each test may be used. FIGS.32A and 32B show an example of a diagnostic procedure for real-timemonitoring that includes 7 tests. Referring to FIG. 32A, the logicbegins at 3200, after the sensor has been inserted/implanted, and an EISprocedure has been performed, so as to provide the EIS data as input. At3200, using the EIS data as input, it is first determined whether thesensor is still in place. Thus, if the |Z| slope is found to be constantacross the tested frequency band (or range), and/or the phase angle isabout −90°, it is determined that the sensor is no longer in place, andan alert is sent, e.g., to the patient/user, indicating that sensorpullout has occurred. If, on the other hand, the sensor is determined tobe in place, the logic moves to initiation of diagnostic checks (3202).

At 3205, Test 1 is similar to Test 1 of the diagnostic procedurediscussed above in connection with FIG. 31, except that the instant Test1 specifies that the later measurement Z_(n) is taken 2 hours after thefirst measurement. As such, in this example, Z_(n)=Z_(2 hr). Morespecifically, Test 1 compares the real impedance 2 hours after (sensorimplantation and) initialization to the pre-initialization value.Similarly, the second part of Test 1 asks whether the difference betweenthe phase 2 hours after initialization and the pre-initialization phaseis greater than 10° at 0.1 Hz. As before, if the answer to either one ofthe inquiries is affirmative, then it is determined that the sensor ishydrated normally and initialized, and Test 1 is satisfied; otherwise,the sensor fails this test. It should be noted that, even though theinstant test inquires about impedance and phase change 2 hours afterinitialization, the time interval between any two consecutive EIS runsmay be shorter or longer, depending on a variety of factors, including,e.g., sensor design, the level of electrode redundancy, the degree towhich the diagnostic procedure includes redundant tests, battery power,etc.

Moving to 3210, the logic next performs a sensitivity-loss check byinquiring whether, after a 2-hour interval (n+2), the percentage changein impedance magnitude at 1 kHz, as well as that in the Isig, is greaterthan 30%. If the answer to both inquiries is “yes”, then it isdetermined that the sensor is losing sensitivity and, as such, Test 2 isdetermined to be failed. It is noted that, although Test 2 isillustrated herein based on a preferred percentage difference of 30%, inother embodiments, the percentage differences in the impedance magnitudeat 1 kHz and in the Isig may fall within the range 10%-50% for purposesof conducting this test.

Test 3 (at 3220) is similar to Test 5 of the algorithm illustrated inFIG. 31. Here, as before, the question is whether the low-frequencyNyquist slope is globally increasing from 0.1 Hz to 1 Hz. If it is, thenthis test is passed; otherwise, the test is failed. As shown in 3220,this test is also amenable to setting a threshold, or an acceptablerange, for the percent change in the low-frequency Nyquist slope, beyondwhich the sensor may be deemed to be failed or, at the very least, maytrigger further diagnostic testing. In embodiments of the invention,such threshold value/acceptable range for the percent change inlow-frequency Nyquist slope may fall within a range of about 2% to about20%. In some preferred embodiments, the threshold value may be about 5%.

The logic next moves to 3230, which is another low-frequency test, thistime involving the phase and the impedance magnitude. More specifically,the phase test inquires whether the phase at 0.1 Hz is continuouslyincreasing over time. If it is, then the test is failed. As with othertests where the parameter's trending is monitored, the low-frequencyphase test of Test 4 is also amenable to setting a threshold, or anacceptable range, for the percent change in the low-frequency phase,beyond which the sensor may be deemed to be failed or, at the veryleast, raise a concern. In embodiments of the invention, such thresholdvalue/acceptable range for the percent change in low-frequency phase mayfall within a range of about 5% to about 30%. In some preferredembodiments, the threshold value may be about 10%.

As noted, Test 4 also includes a low-frequency impedance magnitude test,where the inquiry is whether the impedance magnitude at 0.1 Hz iscontinuously increasing over time. If it is, then the test is failed. Itis noted that Test 4 is considered “failed” if either the phase test orthe impedance magnitude test is failed. The low-frequency impedancemagnitude test of Test 4 is also amenable to setting a threshold, or anacceptable range, for the percent change in the low-frequency impedancemagnitude, beyond which the sensor may be deemed to be failed or, at thevery least, raise a concern. In embodiments of the invention, suchthreshold value/acceptable range for the percent change in low-frequencyimpedance magnitude may fall within a range of about 5% to about 30%. Insome preferred embodiments, the threshold value may be about 10%, wherethe range for impedance magnitude in normal sensors is generally betweenabout 100 KOhms and about 200 KOhms.

Test 5 (at 3240) is another sensitivity loss check that may be thoughtof as supplemental to Test 2. Here, if both the percentage change in theIsig and the percentage change in the impedance magnitude at 1 kHz aregreater than 30%, then it is determined that the sensor is recoveringfrom sensitivity loss. In other words, it is determined that the sensorhad previously undergone some sensitivity loss, even if the sensitivityloss was not, for some reason, detected by Test 2. As with Test 2,although Test 5 is illustrated based on a preferred percentagedifference of 30%, in other embodiments, the percentage differences inthe Isig and the impedance magnitude at 1 kHz may fall within the range10%-50% for purposes of conducting this test.

Moving to 3250, Test 6 provides a sensor functionality test withspecific failure criteria that have been determined based on observeddata and the specific sensor design. Specifically, in one embodiment, asensor may be determined to have failed and, as such, to be unlikely torespond to glucose, if at least two out of the following three criteriaare met: (1) Isig is less than 10 nA; and (2) the imaginary impedance at1 kHz is less than −1500 Ohm; and (3) the phase at 1 kHz is less than−15°. Thus, Test 6 is determined to have been passed if any two of(1)-(3) are not met. It is noted that, in other embodiments, the Isigprong of this test may be failed if the Isig is less than about 5 nA toabout 20 nA. Similarly, the second prong may be failed if the imaginaryimpedance at 1 kHz is less than about −1000 Ohm to about −2000 Ohms.Lastly, the phase prong may be failed if the phase at 1 kHz is less thanabout −10° to about −20°.

Lastly, step 3260 provides another sensitivity check, wherein theparameters are evaluated at low frequency. Thus, Test 7 inquireswhether, at 0.1 Hz, the magnitude of the difference between the ratio ofthe imaginary impedance to the Isig (n+2), on the one hand, and thepervious value of the ratio, on the other, is larger than 30% of themagnitude of the previous value of the ratio. If it is, then the test isfailed; otherwise, the test is passed. Here, although Test 7 isillustrated based on a preferred percentage difference of 30%, in otherembodiments, the percentage difference may fall within the range 10%-50%for purposes of conducting this test.

Once all 7 tests have been implemented, a decision is made at 3270 as towhether the sensor is operating normally, or whether an alert should besent out, indicating that the sensor has failed (or may be failing). Asshown, in this embodiment, a sensor is determined to be functioningnormally (3272) if it passes at least 4 out of the 7 tests. Put anotherway, in order to be determined to have failed, or to at least raise aconcern (3274), the sensor must fail at least 4 out of the 7 tests. Ifit is determined that the sensor is “bad” (3274), an alert to thateffect may be sent, e.g., to the patient/user. As noted previously, inalternative embodiments, a different rule may be used to assess normaloperation versus sensor failure/concern. In addition, in embodiments ofthe invention, each of the tests may be weighted, such that the assignedweight reflects, e.g., the importance of that test, or of the specificparameter(s) queried for that test, in determining overall sensoroperation (normal vs. failed).

As was noted previously, in embodiments of the invention, various of theabove-described impedance-related parameters may be used, eitherindividually or in combination, as inputs into one or more fusionalgorithms for generating more reliable sensor glucose values.Specifically, it is known that, unlike a single-sensor (i.e., asingle-working-electrode) system, multiple sensing electrodes providehigher-reliability glucose readouts, as a plurality of signals, obtainedfrom two or more working electrodes, may be fused to provide a singlesensor glucose value. Such signal fusion utilizes quantitative inputsprovided by EIS to calculate the most reliable output sensor glucosevalue from the redundant working electrodes. It is noted that, while theensuing discussion may describe various fusion algorithms in terms of afirst working electrode (WE1) and a second working electrode (WE2) asthe redundant electrodes, this is by way of illustration, and notlimitation, as the algorithms and their underlying principles describedherein are applicable to, and may be used in, redundant sensor systemshaving more than 2 working electrodes.

FIGS. 33A and 33B show top-level flowcharts for two alternativemethodologies, each of which includes a fusion algorithm. Specifically,FIG. 33A is a flowchart involving a current (Isig)-based fusionalgorithm, and FIG. 33B is a flowchart directed to sensor glucose (SG)fusion. As may be seen from the diagrams, the primary difference betweenthe two methodologies is the time of calibration. Thus, FIG. 33A showsthat, for Isig fusion, calibration 3590 is performed after the fusion3540 is completed. That is, redundant Isigs from WE1 to WEn are fusedinto a single Isig 3589, which is then calibrated to produce a singlesensor glucose value 3598. For SG fusion, on the other hand, calibration3435 is completed for each individual Isig from WE1 to WEn to producecalibrated SG values (e.g., 3436, 3438) for each of the workingelectrodes. Thus, SG fusion algorithms provide for independentcalibration of each of the plurality of Isigs, which may be preferred inembodiments of the invention. Once calibrated, the plurality ofcalibrated SG values is fused into a single SG value 3498.

It is important to note that each of flowcharts shown in FIGS. 33A and33B includes a spike filtering process (3520, 3420). As was describedabove in the discussion relating to sensitivity loss, 1 kHz orhigher-frequency impedance measurements typically cause EIS-inducedspikes in the Isig. Therefore, once an EIS procedure has been performedfor each of the electrodes WE1 to WEn, for both SG fusion and Isigfusion, it is preferable to first filter the Isigs 3410, 3412, etc. and3510, 3512, etc. to obtain respective filtered Isigs 3422, 3424, etc.and 3522, 3524, etc. The filtered Isigs are then either used in Isigfusion, or first calibrated and then used in SG fusion, as detailedbelow. As will become apparent in the ensuing discussion, both fusionalgorithms entail calculation and assignment of weights based on variousfactors.

FIG. 34 shows the details of the fusion algorithm 3440 for SG fusion.Essentially, there are four factors that need to be checked before thefusion weights are determined. First, integrity check 3450 involvesdetermining whether each of the following parameters is within specifiedranges for normal sensor operation (e.g., predetermined lower and upperthresholds): (i) Isig; (ii) 1 kHz real and imaginary impedances; (iii)0.105 Hz real and imaginary impedances; and (iv) Nyquist slope. Asshown, integrity check 3450 includes a Bound Check 3452 and a NoiseCheck 3456, wherein, for each of the Checks, the above-mentionedparameters are used as input parameters. It is noted that, for brevity,real and/or imaginary impedances, at one or more frequencies, appear onFIGS. 33A-35 simply as “Imp” for impedance. In addition, both real andimaginary impedances may be calculated using impedance magnitude andphase (which is also shown as an input on FIGS. 33A and 33B).

The output from each of the Bound Check 3452 and the Noise Check 3458 isa respective reliability index (RI) for each of the redundant workingelectrodes. Thus, the output from the Bound Check includes, e.g.,RI_bound_We₁ (3543) and RI_bound_We₂ (3454). Similarly, for the NoiseCheck, the output includes, e.g., RI_noise_We₁ (3457) and RI_noise_We₂(3458). The bound and noise reliability indices for each workingelectrode are calculated based on compliance with the above-mentionedranges for normal sensor operation. Thus, if any of the parameters fallsoutside the specified ranges for a particular electrode, the reliabilityindex for that particular electrode decreases.

It is noted that the threshold values, or ranges, for theabove-mentioned parameters may depend on various factors, including thespecific sensor and/or electrode design. Nevertheless, in one preferredembodiment, typical ranges for some of the above-mentioned parametersmay be, e.g., as follows: Bound threshold for 1 kHz realimpedance=[0.3e+4 2e+4]; Bound threshold for 1 kHz imaginaryimpedance=[−2e+3, 0]; Bound threshold for 0.105 Hz real impedance=[2e+47e+4]; Bound threshold for 0.105 Hz imaginary impedance=[−2e+5−0.25e+5];and Bound threshold for Nyquist slope=[2 5]. Noise may be calculated,e.g., using second order central difference method where, if noise isabove a certain percentage (e.g., 30%) of median value for each variablebuffer, it is considered to be out of noise bound.

Second, sensor dips may be detected using sensor current (Isig) and 1kHz real impedance. Thus, as shown in FIG. 34, Isig and “Imp” are usedas inputs for dips detection 3460. Here, the first step is to determinewhether there is any divergence between Isigs, and whether any suchdivergence is reflected in 1 kHz real impedance data. This may beaccomplished by using mapping 3465 between the Isig similarity index(RI_sim_isig12) 3463 and the 1 kHz real impedance similarity index(RI_sim_imp12) 3464. This mapping is critical, as it helps avoid falsepositives in instances where a dip is not real. Where the Isigdivergence is real, the algorithm will select the sensor with the higherIsig.

In accordance with embodiments of the invention, thedivergence/convergence of two signals (e.g., two Isigs, or two 1 kHzreal impedance data points) can be calculated as follows:

diff_va1=abs(va1−(va1+va2)/2);

diff_va2=abs(va2−(va1+va2)/2);

RI_sim=1−(diff_va1+diff_va2)/(mean(abs(va1+va2))/4)

where va1 and va2 are two variables, and RI_sim (similarity index) isthe index to measure the convergence or divergence of the signals. Inthis embodiment, RI_sim must be bound between 0 and 1. Therefore, ifRI_sim as calculated above is less than 0, it will be set to 0, and ifit is higher than 1, it will be set to 1.

The mapping 3465 is performed by using ordinary linear regression (OLR).However, when OLR does not work well, a robust median slope linearregression (RMSLR) can be used. For Isig similarity index and 1 kHz realimpedance index, for example, two mapping procedures are needed: (i) MapIsig similarity index to 1 kHz real impedance similarity index; and (ii)map 1 kHz real impedance similarity index to Isig similarity index. Bothmapping procedures will generate two residuals: res12 and res21. Each ofthe dip reliability indices 3467, 3468 can then be calculated as:

RI_dip=1−(res12+res21)/(RI_sim_isig+RI_sim_1K_real_impedance).

The third factor is sensitivity loss 3470, which may be detected using 1kHz imaginary impedance trending in, e.g., the past 8 hours. If onesensor's trending turns negative, the algorithm will rely on the othersensor. If both sensors lose sensitivity, then a simple average istaken. Trending may be calculated by using a strong low-pass filter tosmooth over the 1 kHz imaginary impedance, which tends to be noisy, andby using a correlation coefficient or linear regression with respect totime during, e.g., the past 8 hours to determine whether the correlationcoefficient is negative or the slope is negative. Each of thesensitivity loss reliability indices 3473, 3474 is then assigned abinary value of 1 or 0.

The total reliability index (RI) for each of we1, we2, . . . wen iscalculated as follows:

RI_we₁ = RI_dip_we₁ × RI_sensitivity_loss_we₁ × RI_bound_we₁ × RI_noise_we₁RI_we₂ = RI_dip_we₂ × RI_sensitivity_loss_we₂ × RI_bound_we₂ × RI_noise_we₂RI_we₃ = RI_dip_we₃ × RI_sensitivity_loss_we₃ × RI_bound_we₃ × RI_noise_we₃RI_we₄ = RI_dip_we₄ × RI_sensitivity_loss_we₄ × RI_bound_we₄ × RI_noise_we₄     ⋮RI_we_(n) = RI_dip_we_(n) × RI_sensitivity_loss_we_(n) × RI_bound_we_(n) × RI_noise_we_(n)

Having calculated the respective reliability indices of the individualworking electrodes, the weight for each of the electrodes may becalculated as follow:

weight_we₁ = RI_we₁/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₂ = RI_we₂/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₃ = RI_we₃/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))weight_we₄ = RI_we₄/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))     ⋮weight_we_(n) = RI_we_(n)/(RI_we₁ + RI_we₂ + RI_we₃ + RI_we₄ + … + RI_we_(n))

Based on the above, the fused SG 3498 is then calculated as follows:

SG=weight_we ₁×SG_we ₁+weight_we ₂×SG_we ₂+weight_we ₃×SG_we ₃+weight_we₄×SG_we ₄+ . . . +weight_we _(n)×SG_we _(n)

The last factor relates to artifacts in the final sensor readout, suchas may be caused by instant weight change of sensor fusion. This may beavoided by either applying a low-pass filter 3480 to smooth the RI foreach electrode, or by applying a low-pass filter to the final SG. Whenthe former is used, the filtered reliability indices—e.g., RI_We1* andRI_We2* (3482, 3484)—are used in the calculation of the weight for eachelectrode and, therefore, in the calculation of the fused SG 3498.

FIG. 35 shows the details of the fusion algorithm 3540 for Isig fusion.As can be seen, this algorithm is substantially similar to the one shownin FIG. 34 for SG fusion, with two exceptions. First, as was notedpreviously, for Isig fusion, calibration constitutes the final step ofthe process, where the single fused Isig 3589 is calibrated to generatea single sensor glucose value 3598. See also FIG. 33B. Second, whereasSG fusion uses the SG values for the plurality of electrodes tocalculate the final SG value 3498, the fused Isig value 3589 iscalculated using the filtered Isigs (3522, 3524, and so on) for theplurality of electrodes.

In one closed-loop study involving a non-diabetic population, it wasfound that the above-described fusion algorithms provided considerableimprovements in the Mean Absolute Relative Difference (MARD) both on Day1, when low start-up issues are most significant and, as such, may havea substantial impact on sensor accuracy and reliability, and overall(i.e., over a 7-day life of the sensor). The study evaluated data for an88% distributed layout design with high current density (nominal)plating using three different methodologies: (1) calculation of onesensor glucose value (SG) via fusion using Medtronic Minimed's FerrariAlgorithm 1.0 (which is a SG fusion algorithm as discussed above); (2)calculation of one SG by identifying the better ISIG value using 1 kHzEIS data (through the Isig fusion algorithm discussed above); and (3)calculation of one SG by using the higher ISIG value (i.e., withoutusing EIS). The details of the data for the study are presented below:

(1) SG Based on Ferrari 1.0 Alg for 88% Distributed Layout with HighCurrent Density (Nominal) Plating

Day 1 2 3 4 5 6 7 Total Mean-ARD Percentage 040-080 19.39 17.06 22.2717.50 37.57 11.43 19.69 080-120 19.69 09.18 09.34 08.64 10.01 08.3111.33 11.56 120-240 19.01 17.46 12.44 07.97 11.75 08.82 12.15 12.92240-400 10.25 08.36 14.09 10.86 12.84 22.70 12.88 Total 19.52 11.7110.14 09.30 10.83 09.49 11.89 12.28 Mean-Absolute Bias (sg-bg) 040-08014.86 11.78 15.81 11.07 29.00 07.26 14.05 080-120 19.53 09.37 09.4908.78 09.88 08.44 11.61 11.62 120-240 30.04 29.73 19.34 14.45 18.2512.66 18.89 20.60 240-400 26.75 22.23 39.82 29.00 33.00 61.36 35.19Total 21.62 15.20 12.79 13.21 12.04 10.84 15.04 14.79 Mean-Signed Bias(sg-bg) 040-080 12.15 09.78 15.81 11.07 29.00 07.26 13.01 080-120 −04.45−04.92 −00.90 00.18 01.21 00.85 00.03 −01.44 120-240 −10.18 −27.00−16.89 −02.91 −05.40 −01.24 −11.58 −10.71 240-400 11.25 02.23 −00.07−27.00 −33.00 −61.36 −10.29 Total −04.81 −09.77 −05.09 −00.23 −00.2200.67 −04.98 −03.56 Eval Points 040-080 007 004 000 002 006 003 004 026080-120 090 064 055 055 067 056 047 434 120-240 028 025 022 021 016 032026 170 240-400 000 002 004 008 003 001 002 020 Total 125 095 081 086092 092 079 650

(2) SG Based on Better ISIG Using 1 kHz EIS for 88% Distributed Layoutwith High Current Density (Nominal) Plating

Day 1 2 3 4 5 6 7 Total Mean-ARD Percentage 040-080 16.66 18.78 21.1316.21 43.68 09.50 18.14 080-120 16.22 11.96 08.79 10.49 09.75 08.0410.34 11.36 120-240 15.08 17.50 12.68 07.72 08.74 08.84 13.02 12.16240-400 07.66 06.42 11.10 07.52 15.95 21.13 09.84 Total 15.96 13.7009.92 09.95 09.96 09.40 11.31 11.83 Mean-Absolute Bias (sg-bg) 040-08012.71 13.00 15.00 10.17 33.50 06.00 12.83 080-120 15.70 12.17 08.5710.89 09.62 08.26 10.49 11.32 120-240 24.43 29.82 19.43 13.79 14.6012.97 20.27 19.58 240-400 20.00 17.00 32.50 20.00 41.00 60.00 27.29Total 17.72 17.20 12.56 13.55 10.95 11.21 14.12 14.20 Mean-Signed Bias(sg-bg) 040-080 08.71 13.00 15.00 10.17 33.50 06.00 11.67 080-120 −04.30−08.62 −01.11 −03.64 02.52 00.40 −01.56 −02.52 120-240 −11.30 −29.64−17.09 −08.74 −10.87 −07.23 −15.09 −14.05 240-400 20.00 00.50 09.50−17.33 −41.00 −60.00 −03.18 Total −05.30 −12.56 −06.20 −03.63 −00.10−02.29 −06.35 −05.21 Eval Points 040-080 007 004 000 001 006 002 004 024080-120 082 053 044 045 058 043 041 366 120-240 030 022 023 019 015 030022 161 240-400 000 002 004 006 003 001 001 017 Total 119 081 071 071082 076 068 568

(3) SG Based on Higher ISIG for 88% Distributed Layout with High CurrentDensity (Nominal) Plating

Day 1 2 3 4 5 6 7 Total Mean-ARD Percentage 040-080 17.24 19.13 21.1317.31 43.68 10.38 18.79 080-120 17.69 11.77 09.36 10.70 10.19 08.3410.68 11.86 120-240 16.80 17.63 13.04 07.38 09.04 08.52 13.25 12.50240-400 07.47 06.02 10.85 07.52 15.95 21.13 09.63 Total 17.44 13.6010.37 10.00 10.40 09.36 11.66 12.26 Mean-Absolute Bias (sg-bg) 040-08013.14 13.25 15.00 11.00 33.50 06.50 13.29 080-120 17.23 11.98 09.2211.02 10.08 08.59 10.86 11.85 120-240 27.40 30.09 19.75 13.26 14.9312.45 20.65 20.09 240-400 19.50 16.00 32.00 20.00 41.00 60.00 26.82Total 19.53 17.09 13.00 13.35 11.37 11.18 14.53 14.67 Mean-Signed Bias(sg-bg) 040-080 08.29 12.75 15.00 11.00 33.50 06.50 11.79 080-120 −04.72−08.83 −02.35 −01.56 01.75 −00.18 −01.52 −02.70 120-240 −15.13 −29.73−17.67 −08.42 −11.47 −07.03 −15.43 −14.86 240-400 19.50 01.50 06.33−17.33 −41.00 −60.00 −04.12 Total −06.57 −12.70 −07.11 −02.46 −00.63−02.56 −06.47 −05.57 Eval Points 040-080 007 004 000 001 006 002 004 024080-120 083 054 046 048 060 044 042 377 120-240 030 022 024 019 015 031023 164 240-400 000 002 004 006 003 001 001 017 Total 120 082 074 074084 078 070 582

With the above data, it was found that, with the first approach, theMARD (%) on Day 1 was 19.52%, with an overall MARD of 12.28%. For thesecond approach, the Day −1 MARD was 15.96% and the overall MARD was11.83%. Lastly, for the third approach, the MARD was 17.44% on Day 1,and 12.26% overall. Thus, for this design with redundant electrodes, itappears that calculation of SG based on the better ISIG using 1 kHz EIS(i.e., the second methodology) provides the greatest advantage.Specifically, the lower Day −1 MARD may be attributable, e.g., to betterlow start-up detection using EIS. In addition, the overall MARDpercentages are more than 1% lower than the overall average MARD of13.5% for WE1 and WE2 in this study. It is noted that, in theabove-mentioned approaches, data transitions may be handled, e.g., by afiltering method to minimize the severity of the transitions, such as byusing a low-pass filter 3480 as discussed above in connection with FIGS.33A-35.

It bears repeating that sensor diagnostics, including, e.g., assessmentof low start-up, sensitivity-loss, and signal-dip events depends onvarious factors, including the sensor design, number of electrodes(i.e., redundancy), electrode distribution/configuration, etc. As such,the actual frequency, or range of frequencies, for which an EIS-basedparameter may be substantially glucose-independent, and therefore, anindependent marker, or predictor, for one or more of the above-mentionedfailure modes may also depend on the specific sensor design. Forexample, while it has been discovered, as described hereinabove, thatsensitivity loss may be predicted using imaginary impedance at therelatively higher frequencies—where imaginary impedance is substantiallyglucose-independent—the level of glucose dependence, and, therefore, thespecific frequency range for using imaginary impedance as a marker forsensitivity loss, may shift (higher or lower) depending on the actualsensor design.

More specifically, as sensor design moves more and more towards the useof redundant working electrodes, the latter must be of increasinglysmaller sizes in order to maintain the overall size of the sensor. Thesize of the electrodes, in turn, affects the frequencies that may bequeried for specific diagnostics. In this regard, it is important tonote that the fusion algorithms described herein and shown in FIGS.33A-35 are to be regarded as illustrative, and not limiting, as eachalgorithm can be modified as necessary to use EIS-based parameters atfrequencies that exhibit the least amount of glucose dependence, basedon the type of sensor under analysis.

In addition, experimental data indicates that human tissue structure mayalso affect glucose dependence at different frequencies. For example, inchildren, real impedance at 0.105 Hz has been found to be asubstantially glucose-independent indicator for low start-up detection.It is believed that this comes about as a result of a child's tissuestructure changing, e.g., the Warburg impedance, which relates mostly tothe resistive component. See also the subsequent discussion relating tointerferent detection.

Embodiments of the invention herein are also directed to the use of EISin optimizing sensor calibration. By way of background, in currentmethodologies, the slope of a BG vs. Isig plot, which may be used tocalibrate subsequent Isig values, is calculated as follows:

${slope} = \frac{\sum{{{\alpha\beta}\left( {{isig} - {offset}} \right)}{bg}}}{\sum{{\alpha\beta}\left( {{isig} - {offset}} \right)}^{2}}$

where α is an exponential function of a time constant, β is a functionof blood glucose variance, and offset is a constant. For a sensor insteady condition, this method provides fairly accurate results. Asshown, e.g., in FIG. 36, BG and Isig follow a fairly linearrelationship, and offset can be taken as a constant.

However, there are situations in which the above-mentioned linearrelationship does not hold true, such as, e.g., during periods in whichthe sensor experiences a transition. As shown in FIG. 37, it is clearthat Isig-BG pairs 1 and 2 are significantly different from pairs 3 and4 in terms of Isig and BG relationship. For these types of conditions,use of a constant offset tends to produce inaccurate results.

To address this issue, one embodiment of the invention is directed tothe use of an EIS-based dynamic offset, where EIS measurements are usedto define a sensor status vector as follows:

V={real_imp_1K,img_imp_1K,Nyquist_slope,Nyquist_R_square}

where all of the elements in the vector are substantially BGindependent. It is noted that Nyquist_R_square is the R square of linearregression used to calculate the Nyquist slope, i.e., the square of thecorrelation coefficient between real and imaginary impedances atrelatively-lower frequencies, and a low R square indicates abnormalityin sensor performance. For each Isig-BG pair, a status vector isassigned. If a significant difference in status vector is detected—e.g.,|V2−V3| for the example shown in FIG. 37—a different offset value isassigned for 3 and 4 when compared to 1 and 2. Thus, by using thisdynamic offset approach, it is possible to maintain a linearrelationship between Isig and BG.

In a second embodiment, an EIS-based segmentation approach may be usedfor calibration. Using the example of FIG. 37 and the vector V, it canbe determined that sensor state during 1 and 2 is signficantly differentfrom sensor state during 3 and 4. Therefore, the calibration buffer canbe divided into two segments, as follows:

Isig_buffer1=[Isig1,Isig2]; BG_buffer1=[BG1,BG2]

Isig_buffer2=[Isig3,Isig3]; BG_buffer2=[BG3,BG3]

Thus, when the sensor operates during 1 and 2, Isig_buffer1 andBG_buffer1 would be used for calibration. However, when the sensoroperates during 3 and 4, i.e., during a transition period, Isig_buffer2and BG_buffer2 would be used for calibration.

In yet another embodiment, an EIS-based dynamic slope approach, whereEIS is used to adjust slope, may be used for calibration purposes. FIG.38A shows an example of how this method can be used to improve sensoraccuracy. In this diagram, the data points 1-4 are discrete bloodglucose values. As can be seen from FIG. 38A, there is a sensor dip 3810between data points 1 and 3, which dip can be detected using the sensorstate vector V described above. During the dip, slope can be adjustedupward to reduce the underreading, as shown by reference numeral 3820 inFIG. 38A.

In a further embodiment, EIS diagnostics may be used to determine thetiming of sensor calibrations, which is quite useful for, e.g,low-startup events, sensitivity-loss events, and other similarsituations. As is known, most current methodologies require regularcalibrations based on a pre-set schedule, e.g., 4 times per day. UsingEIS diagnostics, however, calibrations become event-driven, such thatthey may be performed only as often as necessary, and when they would bemost productive. Here, again, the status vector V may be used todetermine when the sensor state has changed, and to request calibrationif it has, indeed, changed.

More specifically, in an illustrative example, FIG. 38B shows aflowchart for EIS-assisted sensor calibration involving low start-updetection. Using Nyquist slope, 1 kHz real impdance, and a bound check3850 (see, e.g., the previously-described bound check and associatedthreshold values for EIS-based parameters in connection with the fusionalgorithms of FIGS. 33A-35), a reliability index 3853 can be developedfor start-up, such that, when the 1 kHz real impedance 3851 and theNyquist slope 3852 are lower than their corresponding upper bounds,RI_startup=1, and sensor is ready for calibration. In other words, thereliability index 3853 is “high” (3854), and the logic can proceed tocalibration at 3860.

When, on the other hand, the 1 kHz real impedance and the Nyquist slopeare higher than their corresponding upper bounds (or threshold values),RI_startup=0 (i.e., it is “low”), and the sensor is not ready forcalibration (3856), i.e., a low start-up issue may exist. Here, thetrend of 1 kHz real impedance and the Nyquist slope can be used topredict when both parameters will be in range (3870). If it is estimatedthat this will only take a very short amount of time (e.g., less thanone hour), then the algorithm waits until the sensor is ready, i.e.,until the above-mentioned EIS-based parameters are in-bound (3874), atwhich point the algorithm proceeds to calibration. If, however, the waittime would be relatively long (3876), then the sensor can be calibratednow, and then the slope or offset can be gradually adjusted according tothe 1 kHz real impedance and the Nyquist slope trend (3880). It is notedthat by performing the adjustment, serious over- or under-reading causedby low start-up can be avoided. As noted previously, the EIS-basedparameters and related information that is used in the instantcalibration algorithm is substantially glucose-independent.

It is noted that, while the above description in connection with FIG.38B shows a single working electrode, as well as the calculation of areliability index for start-up of that working electrode, this is by wayof illustration, and not limitation. Thus, in a redundant sensorincluding two or more working electrodes, a bound check can beperformed, and a start-up reliability index calculated, for each of theplurality of (redundant) working electrodes. Then, based on therespective reliability indices, at least one working electrode can beidentified that can proceed to obtain glucose measurements. In otherwords, in a sensor having a single working electrode, if the latterexhibits low start-up, actual use of the sensor (for measuring glucose)may have to be delayed until the low start-up period is over. Thisperiod may typically be on the order of one hour or more, which isclearly disadvantageous. In contrast, in a redundant sensor, utilizingthe methodology described herein allows an adaptive, or “smart”,start-up, wherein an electrode that can proceed to data gathering can beidentified in fairly short order, e.g., on the order of a few minutes.This, in turn, reduces MARD, because low start-up generally providesabout a 1/2% increase in MARD.

In yet another embodiment, EIS can aid in the adjustment of thecalibration buffer. For existing calibration algorithms, the buffer sizeis always 4, i.e., 4 Isig-BG pairs, and the weight is based upon awhich, as noted previously, is an exponential function of a timeconstant, and β, which is a function of blood glucose variance. Here,EIS can help to determine when to flush the buffer, how to adjust bufferweight, and what the appropriate buffer size is.

Embodiments of the invention are also directed to the use of EIS forinterferent detection. Specifically, it may be desirable to provide amedication infusion set that includes a combination sensor andmedication-infusion catheter, where the sensor is placed within theinfusion catheter. In such a system, the physical location of theinfusion catheter relative to the sensor may be of some concern, dueprimarily to the potential impact on (i.e., interference with) sensorsignal that may be caused by the medication being infused and/or aninactive component thereof.

For example, the diluent used with insulin contains m-cresol as apreservative. In in-vitro studies, m-cresol has been found to negativelyimpact a glucose sensor if insulin (and, therefore, m-cresol) is beinginfused in close proximity to the sensor. Therefore, a system in which asensor and an infusion catheter are to be combined in a single needlemust be able to detect, and adjust for, the effect of m-cresol on thesensor signal. Since m-cresol affects the sensor signal, it would bepreferable to have a means of detecting this interferent independentlyof the sensor signal itself.

Experiments have shown that the effect of m-cresol on the sensor signalis temporary and, thus, reversible. Nevertheless, when insulin infusionoccurs too close to the sensor, the m-cresol tends to “poison” theelectrode(s), such that the latter can no longer detect glucose, untilthe insulin (and m-cresol) have been absorbed into the patient's tissue.In this regard, it has been found that there is typically about a40-minute time period between initiation of insulin infusion and whenthe sensor has re-gained the ability to detect glucose again. However,advantageously, it has also been discovered that, during the same timeperiod, there is a large increase in 1 kHz impedance magnitude quiteindependently of the glucose concentration.

Specifically, FIG. 39 shows Isig and impedance data for an in-vitroexperiment, wherein the sensor was placed in a 100 mg/dL glucosesolution, and 1 kHz impedance was measured every 10 minutes, as shown byencircled data points 3920. m-cresol was then added to bring thesolution to 0.35% m-cresol (3930). As can be seen, once m-cresol hasbeen added, the Isig 3940 initially increases dramatically, and thenbegins to drift down. The concentration of glucose in the solution wasthen doubled, by adding an addition 100 mg/dL glucose. This, however,had no effect on the Isig 3940, as the electrode was unable to detectthe glucose.

On the other hand, the m-cresol had a dramatic effect on both impedancemagnitude and phase. FIG. 40A shows a Bode plot for the phase, and FIG.40B shows a Bode plot for impedance magnitude, for both before and afterthe addition of m-cresol. As can be seen, after the m-cresol was added,the impedance magnitude 4010 increased from its post-initializationvalue 4020 by at least an order of magnitude across the frequencyspectrum. At the same time, the phase 4030 changed completely ascompared to its post-initialization value 4040. On the Nyquist plot ofFIG. 40C. Here, the pre-initialization curve 4050 and thepost-initialization curve 4060 appear as expected for anormally-functioning sensor. However, after the addition of m-cresol,the curve 4070 becomes drastically different.

The above experiment identifies an important practical pitfall ofcontinuing to rely on the Isig after m-cresol has been added. Referringback to FIG. 39, a patient/user monitoring the sensor signal may be putunder the mistaken impression that his glucose level has just spiked,and that he should administer a bolus. The user then administers thebolus, at which the Isig has already started to drift back down. Inother words, to the patient/user, everything may look normal. Inreality, however, what has really happened is that the patient justadministered an unneeded dose of insulin which, depending on thepatient's glucose level prior to administration of the bolus, may putthe patient at risk of experiencing a hypoglycemic event. This scenarioreinforces the desirability of a means of detecting interferents that isas glucose-independent as possible.

FIG. 41 shows another experiment, where a sensor was initialized a 100mg/dL glucose solution, after which glucose was raised to 400 mg/dL forone hour, and then returned to 100 mg/dL. m-cresol was then added toraise the concentration to 0.35%, with the sensor remaining in thissolution for 20 minutes. Finally, the sensor was placed in a 100 mg/dLglucose solution to allow Isig to recover after exposure to m-cresol. Ascan be seen, after initialization, the 1 kHz impedance magnitude 4110was at about 2 kOhms. When m-cresol was added, the Isig 4120 spiked, asdid impedance magnitude 4110. Moreover, when the sensor was returned toa 100 md/dL glucose solution, the impedance magnitude 4110 also returnedto near normal level.

As can be seen from the above experiments, EIS can be used to detect thepresence of an interfering agent—in this case, m-cresol. Specifically,since the interferent affects the sensor in such a way as to increasethe impedance magnitude across the entire frequency spectrum, theimpedance magnitude may be used to detect the interference. Once theinterference has been detected, either the sensor operating voltage canbe changed to a point where the interferent is not measured, or datareporting can be temporarily suspended, with the sensor indicating tothe patient/user that, due to the administration of medication, thesensor is unable to report data (until the measured impedance returns tothe pre-infusion level). It is noted that, since the impact of theinterferent is due to the preservative that is contained in insulin, theimpedance magnitude will exhibit the same behavior as described aboveregardless of whether the insulin being infused is fast-acting or slow.

Importantly, as mentioned above, the impedance magnitude, and certainlythe magnitude at 1 kHz, is substantially glucose-independent. Withreference to FIG. 41, it can be seen that, as the concentration ofglucose is raised from 100 mg/dL to 400 mg/dL—a four-fold increase—the 1kHz impedance magnitude increase from about 2000 Ohms to about 2200Ohms, or about a 10% increase. In other words, the effect of glucose onthe impedance magnitude measurement appears to be about an order ofmagnitude smaller compared to the measured impedance. This level of“signal-to-noise” ratio is typically small enough to allow the noise(i.e., the glucose effect) to be filtered out, such that the resultantimpedance magnitude is substantially glucose-independent. In addition,it should be emphasized that the impedance magnitude exhibits an evenhigher degree of glucose-independence in actual human tissue, ascompared to the buffer solution that was used for the in-vitroexperiments described above.

Embodiments of the invention are also directed to an Analog Front EndIntegrated Circuit (AFE IC), which is a custom Application SpecificIntegrated Circuit (ASIC) that provides the necessary analog electronicsto: (i) support multiple potentiostats and interface with multi-terminalglucose sensors based on either Oxygen or Peroxide; (ii) interface witha microcontroller so as to form a micropower sensor system; and (iii)implement EIS diagnostics, fusion algorithms, and other EIS-basedprocesses based on measurement of EIS-based parameters. Morespecifically, the ASIC incorporates diagnostic capability to measure thereal and imaginary impedance parameters of the sensor over a wide rangeof frequencies, as well as digital interface circuitry to enablebidirectional communication with a microprocessor chip. Moreover, theASIC includes power control circuitry that enables operation at very lowstandby and operating power, and a real-time clock and a crystaloscillator so that an external microprocessor's power can be turned off.

FIGS. 42A and 42B show a block diagram of the ASIC, and Table 1 belowprovides pad signal descriptions (shown on the left-hand side of FIGS.42A and 42B), with some signals being multiplexed onto a single pad.

TABLE 1 Pad signal descriptions Pad Name Functional Description Powerplane VBAT Battery power input 2.0 V to 4.5 V VBAT VDDBU Backup logicpower 1.4 to 2.4 V VDDBU VDD Logic power - 1.6-2.4 V VDD VDDA Analogpower - 1.6-2.4 V VDDA VPAD Pad I/O power - 1.8 V-3.3 V VPAD VSS Logicground return and digital pad return VSSA Analog ground return andanalog pad return ADC_IN1, 2 ADC Inputs, VDDA max input VDDA V1P2B 1.2volt reference Bypass capacitor VDDA nSHUTDN External VDD regulatorcontrol signal. Goes low when battery is VBAT low. VPAD_EN Goes highwhen VPAD IOs are active. Can control external VBAT regulator. DA1, 2DAC outputs VDDA TP_ANA_MUX Mux of analog test port - output or inputVDDA TP_RES External 1 meg ohm calibration resistor & analog test portVDDA WORK1-5 Working Electrodes of Sensor VDDA RE Reference Electrode ofSensor VDDA COUNTER Counter Electrode of Sensor VDDA CMP1_IN Generalpurpose Voltage comparator VDDA CMP2_IN General purpose Voltagecomparator VDDA WAKEUP Debounced interrupt input VBAT XTALI, XTALO32.768 kHz Crystal Oscillator pads VDDA OSC_BYPASS Test clock controlVDDA SEN_CONN_SW Sensor connection switch input. Pulled to VSSA =connection VDDA VPAD_EN Enable the VPAD power and VPAD power plane logicVBAT nRESET_OD Signal to reset external circuitry such as amicroprocessor SPI_CK, SPI interface signals to microprocessor VPADnSPI_CS, SPI_MOIS, SPI_MISO UP_WAKEUP Microprocessor wakeup signal VPADCLK_32KHZ Gated Clock output to external circuitry microprocessor VPADUP_INT Interrupt signal to microprocessor VPAD nPOR1_OUT Backup Power onreset, output from analog VBAT nPOR1_IN VBAT power plane reset, input todigital in battery plane VBAT (VDDBU) nPOR2_OUT VDD POR signal, outputfrom analog VDD nPOR2_OUT_OD VDD POR signal open drain (nfet out only),stretched output VBAT from digital nPOR2_IN VDD power plane logic reset.Is level shifted to VDD inside the VDD chip, input to digital VDD logic.

The ASIC will now be described with reference to FIGS. 42A and 42B andTable 1.

Power Planes

The ASIC has one power plane that is powered by the supply pad VBAT(4210), which has an operating input range from 2.0 volts to 4.5 volts.This power plane has a regulator to lower the voltage for some circuitsin this plane. The supply is called VDDBU (4212) and has an output padfor test and bypassing. The circuits on the VBAT supply include an RCoscillator, real time clock (RC osc) 4214, battery protection circuit,regulator control, power on reset circuit (POR), and variousinputs/outputs. The pads on the VBAT power plane are configured to drawless than 75 nA at 40° C. and VBAT=3.50V.

The ASIC also has a VDD supply to supply logic. The VDD supply voltagerange is programmable from at least 1.6 volts to 2.4 volts. The circuitson the VDD power plane include most of the digital logic, timer (32khz), and real time clock (32 khz). The VDD supply plane includes levelshifters interfacing to the other voltage planes as necessary. The levelshifters, in turn, have interfaces conditioned so that any powered powerplane does not have an increase in current greater than 10 nA if anotherpower plane is unpowered.

The ASIC includes an onboard regulator (with shutdown control) and anoption for an external VDD source. The regulator input is a separatepad, REG_VDD_IN (4216), which has electrostatic discharge (ESD)protection in common with other I/Os on VBAT. The onboard regulator hasan output pad, REG_VDD_OUT (4217). The ASIC also has an input pad forthe VDD, which is separate from the REG_VDD_OUT pad.

The ASIC includes an analog power plane, called VDDA (4218), which ispowered by either the VDD onboard regulator or an external source, andis normally supplied by a filtered VDD. The VDDA supplied circuits areconfigured to operate within 0.1 volt of VDD, thereby obviating the needfor level shifting between the VDDA and VDD power planes. The VDDAsupply powers the sensor analog circuits, the analog measurementcircuits, as well as any other noise-sensitive circuitry.

The ASIC includes a pad supply, VPAD, for designated digital interfacesignals. The pad supply has an operating voltage range from at least 1.8V to 3.3 V. These pads have separate supply pad(s) and are powered froman external source. The pads also incorporate level shifters to otheronboard circuits to allow the flexible pad power supply rangeindependently of the VDD logic supply voltage. The ASIC can conditionthe VPAD pad ring signals such that, when the VPAD supply is notenabled, other supply currents will not increase by more than 10 nA.

Bias Generator

The ASIC has a bias generator circuit, BIAS_GEN (4220), which issupplied from the VBAT power, and which generates bias currents that arestable with supply voltage for the system. The output currents have thefollowing specifications: (i) Supply sensitivity: <±2.5% from a supplyvoltage of 1.6 v to 4.5V; and (ii) Current accuracy: <±3% aftertrimming.

The BIAS_GEN circuit generates switched and unswitched output currentsto supply circuits needing a bias current for operation. The operatingcurrent drain of the BIAS_GEN circuit is less than 0.3 uA at 25° C. withVBAT from 2.5V-4.5V (excluding any bias output currents). Lastly, thetemperature coefficient of the bias current is generally between 4,000ppm/° C. and 6,000 ppm/° C.

Voltage Reference

The ASIC, as described herein is configured to have a low power voltagereference, which is powered from the VBAT power supply. The voltagereference has an enable input which can accept a signal from logicpowered by VBAT or VDDBU. The ASIC is designed such that the enablesignal does not cause any increase in current in excess of 10 nA fromany supply from this signal interface when VBAT is powered.

The reference voltage has the following specifications: (i) Outputvoltage: 1.220±3 mV after trimming; (ii) Supply sensitivity: <±6 mV from1.6 V to 4.5V input; (iii) Temperature sensitivity: <±5 mV from 0° C. to60° C.; and (iv) Output voltage default accuracy (without trim): 1.220V±50 mV. In addition, the supply current is to be less than 800 nA at4.5V, 40° C. In this embodiment, the reference output will be forced toVSSA when the reference is disabled so as to keep the VDD voltageregulator from overshooting to levels beyond the breakdown voltage ofthe logic.

32 kHz Oscillator

The ASIC includes a low power 32.768 kHz crystal oscillator 4222 whichis powered with power derived from the VDDA supply and can trim thecapacitance of the crystal oscillator pads (XTALI, XTALO) with software.Specifically, the frequency trim range is at least −50 ppm to +100 ppmwith a step size of 2 ppm max throughout the trim range. Here, a crystalmay be assumed with a load capacitance of 7 pF, Ls=6.9512 kH, Cs=3.3952fF, Rs=70 k, shunt capacitance=1 pF, and a PC Board parasiticcapacitance of 2 pF on each crystal terminal.

The ASIC has a VPAD level output available on a pad, CLK_32 kHZ, wherethe output can be disabled under software and logic control. The defaultis driving the 32 kHz oscillator out. An input pin, OSC32K_BYPASS(4224), can disable the 32 kHz oscillator (no power drain) and allowsfor digital input to the XTALI pad. The circuits associated with thisfunction are configured so as not add any ASIC current in excess of 10nA in either state of the OSC32K_BYPASS signal other than the oscillatorcurrent when OSC32K_BYPASS is low.

The 32 kHZ oscillator is required to always be operational when the VDDAplane is powered, except for the bypass condition. If the OSC32K_BYPASSis true, the 32 KHZ oscillator analog circuitry is put into a low powerstate, and the XTALI pad is configured to accept a digital input whoselevel is from 0 to VDDA. It is noted that the 32 kHz oscillator outputhas a duty cycle between 40% and 60%.

Timer

The ASIC includes a Timer 4226 that is clocked from the 32 kHzoscillator divided by 2. It is pre-settable and has two programmabletimeouts. It has 24 programmable bits giving a total time count to 17minutes, 4 seconds. The Timer also has a programmable delay to disablethe clock to the CLK_32 KHz pad and set the microprocessor (uP)interface signals on the VPAD plane to a predetermined state (Seesection below on Microprocessor Wakeup Control Signals). This will allowthe microprocessor to go into suspend mode without an external clock.However, this function may be disabled by software with a programmablebit.

The Timer also includes a programmable delay to wakeup themicroprocessor by enabling the CLK_32 KHZ clock output and settingUP_WAKEUP high. A transition of the POR2 (VDD POR) from supply low stateto supply OK state will enable the 32 kHz oscillator, the CLK_32 KHZclock output and set UP_WAKEUP high. The power shutdown and power up areconfigured to be controlled with programmable control bits.

Real Time Clock (RTC)

The ASIC also has a 48 bit readable/writeable binary counter thatoperates from the ungated, free running 32 kHz oscillator. The write tothe real time clock 4228 requires a write to an address with a keybefore the clock can be written. The write access to the clock isconfigured to terminate between 1 msec and 20 msec after the write tothe key address.

The real time clock 4228 is configured to be reset by a power on reseteither by POR1_IN (the VBAT POR) or POR2_IN (the VDD POR) to half count(MSB=1, all other bits 0). In embodiments of the invention, the realtime clock has programmable interrupt capability, and is designed to berobust against single event upsets (SEUs), which may be accomplishedeither by layout techniques or by adding capacitance to appropriatenodes, if required.

RC Oscillator

The ASIC further includes an RC clock powered from the VBAT supply orVBAT derived supply. The RC Oscillator is always running, except thatthe oscillator can be bypassed by writing to a register bit in analogtest mode (see section on Digital Testing) and applying a signal to theGPIO_VBAT with a 0 to VBAT level. The RC oscillator is not trimmable,and includes the following specifications: (i) a frequency between 750Hz and 1500 Hz; (ii) a duty cycle between 50%±10%; (iii) currentconsumption of less than 200 nA at 25° C.; (iv) frequency change of lessthan ±2% from 1V to 4.5V VBAT supply and better than 1% from 1.8V to4.5V VBAT supply; and (v) frequency change of less than +2, −2% from atemperature of 15° C. to 40° C. with VBAT=3.5V. The RC frequency can bemeasured with the 32 kHz crystal oscillator or with an externalfrequency source (See Oscillator Calibration Circuit).

Real Time RC Clock (RC Oscillator Based)

The ASIC includes a 48 bit readable/writeable binary ripple counterbased on the RC oscillator. A write to the RC real time clock requires awrite to an address with a key before the clock can be written. Thewrite access to the clock terminates between 1 msec and 20 msec afterthe write to the key address, wherein the time for the protection windowis configured to be generated with the RC clock.

The real time RC clock allows for a relative time stamp if the crystaloscillator is shutdown, and is configured to be reset on POR1_IN (theBAT POR) to half count (MSB=1, all others 0). The real time RC clock isdesigned to be robust against single event upsets (SEUs) either bylayout techniques or by adding capacitance to appropriate nodes, whererequired. On the falling edge of POR2_IN, or if the ASIC goes intoBattery Low state, the RT real time clock value may be captured into aregister that can be read via the SPI port. This register and associatedlogic are on the VBAT or VDDBU power plane.

Battery Protection Circuit

The ASIC includes a battery protection circuit 4230 that uses acomparator to monitor the battery voltage and is powered with powerderived from the VBAT power plane. The battery protection circuit isconfigured to be always running with power applied to the VBAT supply.The battery protection circuit may use the RC oscillator for clockingsignals, and have an average current drain that is less than 30 nA,including a 3 MOhm total resistance external voltage divider.

The battery protection circuit uses an external switched voltage dividerhaving a ratio of 0.421 for a 2.90V battery threshold. The ASIC also hasan internal voltage divider with the ratio of 0.421±0.5%. This divideris connected between BATT_DIV_EN (4232) and VSSA (4234), and the divideroutput is a pin called BATT_DIV_INT (4236). To save pins in the packagedpart, the BATT_DIV_INT in this embodiment is connected to BATT_DIVinternally in the package. Also in this configuration, BATT_DIV_EN doesnot need to come out of the package, saving two package pins.

The battery protection circuit is configured to sample the voltage on aninput pin, BATT_DIV (4238), at approximately 2 times per second, whereinthe sample time is generated from the RC Oscillator. The ASIC is able toadjust the divider of the RC Oscillator to adjust the sampling timeinterval to 0.500 sec±5 msec with the RC oscillator operating within itsoperating tolerance. In a preferred embodiment, the ASIC has a test modewhich allows more frequent sampling intervals during test.

The comparator input is configured to accept an input from 0 to VBATvolts. The input current to the comparator input, BATT_DIV, is less than10 nA for inputs from 0 to VBAT volts. The comparator sampling circuitoutputs to a pad, BATT_DIV_EN, a positive pulse which can be used byexternal circuitry to enable an off-chip resistor divider only duringthe sampling time to save power. The voltage high logic level is theVBAT voltage and the low level is VSS level.

The output resistance of the BATT_DIV_EN pad shall be less than 2 kOhmsat VBAT=3.0V. This allows the voltage divider to be driven directly fromthis output. After a programmable number of consecutive samplesindicating a low battery condition, the comparator control circuitrytriggers an interrupt to the interrupt output pad, UP_INT. The defaultnumber of samples is 4, although the number of consecutive samples isprogrammable from 4 to 120.

After a programmable number of consecutive samples indicating a lowbattery after the generation of the UP_INT above, the comparator controlcircuitry is configured to generate signals that will put the ASIC intoa low power mode: The VDD regulator will be disabled and a low signalwill be asserted to the pad, VPAD_EN. This will be called the BatteryLow state. Again, the number of consecutive samples is programmable from4 to 120 samples, with the default being 4 samples.

The comparator has individual programmable thresholds for falling andrising voltages on BATT_DIV. This is implemented in the digital logic tomultiplex the two values to the circuit depending on the state of theBattery Low state. Thus, if Battery Low state is low, the fallingthreshold applies, and if the Battery Low state is high, the risingthreshold applies. Specifically, the comparator has 16 programmablethresholds from 1.22 to 1.645±3%, wherein the DNL of the programmablethresholds is set to be less than 0.2 LSB.

The comparator threshold varies less than +/−1% from 20° C. to 40° C.The default threshold for falling voltage is 1.44V (VBAT threshold of3.41V with nominal voltage divider), and the default threshold forrising voltage is 1.53V (VBAT threshold of 3.63V with nominal voltagedivider). After the ASIC has been put into the Battery Low state, if thecomparator senses 4 consecutive indications of battery OK, then the ASICwill initiate the microprocessor startup sequence.

Battery Power Plane Power On Reset

A power on reset (POR) output is generated on pad nPOR1_OUT (4240) ifthe input VBAT slews more than 1.2 volt in a 50 usec period or if theVBAT voltage is below 1.6±0.3 volts. This POR is stretched to a minimumpulse width of 5 milliseconds. The output of the POR circuit isconfigured to be active low and go to a pad, nPOR1_OUT, on the VBATpower plane.

The IC has an input pad for the battery power plane POR, nPOR1_IN(4242). This input pad has RC filtering such that pulses shorter than 50nsec will not cause a reset to the logic. In this embodiment, nPOR1_OUTis externally connected to the nPOR1_IN in normal operation, therebyseparating the analog circuitry from the digital circuitry for testing.The nPOR1_IN causes a reset of all logic on any of the power planes, andinitializes all registers to their default value. Thus, the reset statusregister POR bit is set, and all other reset status register bits arecleared. The POR reset circuitry is configured so as not to consume morethan 0.1 uA from VBAT supply for time greater than 5 seconds after powerup.

VDD Power On Reset (POR)

The ASIC also has a voltage comparator circuit which generates a VDDvoltage plane reset signal upon power up, or if the VDD drops below aprogrammable threshold. The range is programmable with several voltagethresholds. The default value is 1.8V-15% (1.53V). The POR2 has aprogrammable threshold for rising voltage, which implements hysteresis.The rising threshold is also programmable, with a default value of1.60V±3%.

The POR signal is active low and has an output pad, nPOR2_OUT (4244), onthe VDD power plane. The ASIC also has an active low POR open drainoutput, nPOR2_OUT_OD (4246), on the VBAT power plane. This could be usedfor applying POR to other system components.

The VDD powered logic has POR derived from the input pad, nPOR2_IN(4248). The nPOR2_IN pad is on the VDD power plane, and has RC filteringsuch that pulses shorter than 50 nsec will not cause a reset to thelogic. The nPOR2_OUT is configured be externally connected to thenPOR2_IN input pad under normal usage, thereby separating the analogcircuitry from the digital circuitry.

The reset which is generated is stretched to at least 700 msec of activetime after VDD goes above the programmable threshold to assure that thecrystal oscillator is stable. The POR reset circuitry is to consume nomore than 0.1 uA from the VDD supply for time greater than 5 secondsafter power up, and no more than 0.1 uA from VBAT supply for timegreater than 5 seconds after power up. The register that stores the PORthreshold value is powered from the VDD power plane.

Sensor Interface Electronics

In an embodiment of the invention, the sensor circuitry supports up tofive sensor WORK electrodes (4310) in any combination of peroxide oroxygen sensors, although, in additional embodiments, a larger number ofsuch electrodes may also be accommodated. While the peroxide sensor WORKelectrodes source current, the oxygen sensor WORK electrodes sinkcurrent. For the instant embodiment, the sensors can be configured inthe potentiostat configuration as shown in FIG. 43.

The sensor electronics have programmable power controls for eachelectrode interface circuit to minimize current drain by turning offcurrent to unused sensor electronics. The sensor electronics alsoinclude electronics to drive a COUNTER electrode 4320 that uses feedbackfrom a RE (reference) electrode 4330. The current to this circuitry maybe programmed off when not in use to conserve power. The interfaceelectronics include a multiplexer 4250 so that the COUNTER and REelectrodes may be connected to any of the (redundant) WORK electrodes.

The ASIC is configured to provide the following Sensor Interfaces: (i)RE: Reference electrode, which establishes a reference potential of thesolution for the electronics for setting the WORK voltages; (ii)WORK1-WORK5: Working sensor electrodes where desired reduction/oxidation(redox) reactions take place; and (iii) COUNTER: Output from this padmaintains a known voltage on the RE electrode relative to the systemVSS. In this embodiment of the invention, the ASIC is configured so asto be able to individually set the WORK voltages for up to 5 WORKelectrodes with a resolution and accuracy of better than or equal to 5mV.

The WORK voltage(s) are programmable between at least 0 and 1.22Vrelative to VSSA in the oxygen mode. In the peroxide mode, the WORKvoltage(s) are programmable between at least 0.6 volt and 2.054 voltsrelative to VSSA. If the VDDA is less than 2.15V, the WORK voltage isoperational to VDDA −0.1V. The ASIC includes current measuring circuitsto measure the WORK electrode currents in the peroxide sensor mode. Thismay be implemented, e.g., with current-to-voltage orcurrent-to-frequency converters, which may have the followingspecifications: (i) Current Range: 0-300 nA; (ii) Voltage output range:Same as WORK electrode in peroxide/oxygen mode; (iii) Output offsetvoltage: ±5 mV max; and (iv) Uncalibrated resolution: ±0.25 nA.

Current Measurement Accuracy after applying a calibration factor to thegain and assuming an acquisition time of 10 seconds or less is:

-   -   5 pA-1 nA: ±3%±20 pA    -   1 nA-10 nA: ±3%±20 pA    -   10 nA-300 nA: ±3%±0.2 nA

For current-to-frequency converters (ItoFs) only, the frequency rangemay be between 0 Hz and 50 kHz. The current converters must operate inthe specified voltage range relative to VSS of WORK electrodes in theperoxide mode. Here, the current drain is less than 2 uA from a 2.5Vsupply with WORK electrode current less than 10 nA per converterincluding digital-to-analog (DAC) current.

The current converters can be enabled or disabled by software control.When disabled, the WORK electrode will exhibit a very high impedancevalue, i.e., greater than 100 Mohm. Again, for ItoFs only, the output ofthe I-to-F converters will go to 32 bit counters, which can be read,written to, and cleared by the microprocessor and test logic. During acounter read, clocking of the counter is suspended to ensure an accurateread.

In embodiments of the invention, the ASIC also includes currentmeasuring circuits to measure the WORK electrode currents in the oxygensensor mode. The circuit may be implemented as a current-to-voltage or acurrent-to-frequency converter, and a programmable bit may be used toconfigure the current converters to operate in the oxygen mode. Asbefore, the current converters must operate in the specified voltagerange of the WORK electrodes relative to VSS in the oxygen mode. Here,again, the current range is 3.7 pA-300 nA, the voltage output range isthe same as WORK electrode in oxygen mode, the output offset voltage is±5 mV max, and the uncalibrated resolution is 3.7 pA±2 pA.

Current Measurement Accuracy after applying a calibration factor to thegain and assuming an acquisition time of 10 seconds or less is:

-   -   5 pA-1 nA: ±3%±20 pA    -   1 nA-10 nA: ±3%±20 pA    -   10 nA-300 nA: ±3%±0.2 nA

For current-to-frequency converters (ItoFs) only, the frequency rangemay be between 0 Hz and 50 kHz, and the current drain is less than 2 uAfrom a 2.5V supply with WORK electrode current less than 10 nA perconverter, including DAC current. The current converters can be enabledor disabled by software control. When disabled, the WORK electrode willexhibit a very high impedance value, i.e., greater than 100 Mohm. Also,for ItoFs only, the output of the I-to-F converters will go to 32 bitcounters, which can be read, written to, and cleared by themicroprocessor and test logic. During a counter read, clocking of thecounter is suspended to ensure an accurate read.

In embodiments of the invention, the Reference electrode (RE) 4330 hasan input bias current of less than 0.05 nA at 40° C. The COUNTERelectrode adjusts its output to maintain a desired voltage on the REelectrode. This is accomplished with an amplifier 4340 whose output tothe COUNTER electrode 4320 attempts to minimize the difference betweenthe actual RE electrode voltage and the target RE voltage, the latterbeing set by a DAC.

The RE set voltage is programmable between at least 0 and 1.80V, and thecommon mode input range of the COUNTER amplifier includes at least 0.20to (VDD−0.20)V. A register bit may be used to select the common modeinput range, if necessary, and to provide for programming the mode ofoperation of the COUNTER. The WORK voltage is set with a resolution andaccuracy of better than or equal to 5 mV. It is noted that, in thenormal mode, the COUNTER voltage seeks a level that maintains the REvoltage to the programmed RE target value. In the force counter mode,however, the COUNTER electrode voltage is forced to the programmed REtarget voltage.

All electrode driving circuits are configured to be able to drive theelectrode to electrode load and be free from oscillation for any usescenario. FIG. 44 shows the equivalent ac inter-electrode circuitaccording to the embodiment of the invention with the potentiostatconfiguration as shown in FIG. 43. The equivalent circuit shown in FIG.44 may be between any of the electrodes, i.e., WORK1-WORK5, COUNTER andRE, with value ranges as follows for the respective circuit components:

-   -   Ru=[200-5 k] Ohms    -   Cc=[10-2000] pF    -   Rpo=[1-20] kOhms    -   Rf=[200-2000] kOhms    -   Cf=[2-30] uF

During initialization, the drive current for WORK electrodes and theCOUNTER electrode need to supply higher currents than for the normalpotentiostat operation described previously. As such, programmableregister bits may be used to program the electrode drive circuits to ahigher power state if necessary for extra drive. It is important toachieve low power operation in the normal potentiostat mode, where theelectrode currents are typically less than 300 nA.

In preferred embodiments, during initialization, the WORK1 through WORK5electrodes are programmable in steps equal to, or less than, 5 mV from 0to VDD volts, and their drive or sink current output capability is aminimum of 20 uA, from 0.20V to (VDD−0.20V). Also during initialization,the ASIC is generally configured to be able to measure the current ofone WORK electrode up to 20 uA with an accuracy of ±2%±40 nA of themeasurement value. Moreover, during initialization, the RE set voltageis programmable as described previously, the COUNTER DRIVE CIRCUIToutput must be able to source or sink 50 uA minimum with the COUNTERelectrode from 0.20V to (VDD−0.20V), and the supply current (VDD andVDDA) to the initialization circuitry is required to be less than 50 uAin excess of any output current sourced.

Current Calibrator

In embodiments of the invention, the ASIC has a current reference thatcan be steered to any WORK electrode for the purpose of calibration. Inthis regard, the calibrator includes a programmable bit that causes thecurrent output to sink current or source current. The programmablecurrents include at least 10 nA, 100 nA, and 300 nA, with an accuracy ofbetter than ±1%±1 nA, assuming a 0 tolerance external precisionresistor. The calibrator uses a 1 MegOhm precision resistor connected tothe pad, TP_RES (4260), for a reference resistance. In addition, thecurrent reference can be steered to the COUNTER or RE electrodes for thepurpose of initialization and/or sensor status. A constant current maybe applied to the COUNTER or the RE electrodes and the electrode voltagemay be measured with the ADC.

High Speed RC Oscillator

With reference back to FIG. 42, the ASIC further includes a high speedRC oscillator 4262 which supplies the analog-to-digital converter (ADC)4264, the ADC sequencer 4266, and other digital functions requiring ahigher speed clock than 32 kHz. The high speed RC oscillator is phasedlocked to the 32 kHz clock (32.768 kHz) to give an output frequencyprogrammable from 524.3 kHz to 1048 kHz. In addition, the high speed RCoscillator has a duty cycle of 50%±10%, a phase jitter of less than 0.5%rms, a current of less than 10 uA, and a frequency that is stablethrough the VDD operating range (voltage range of 1.6 to 2.5V). Thedefault of the high speed RC oscillator is “off” (i.e., disabled), inwhich case the current draw is less than 10 nA. However, the ASIC has aprogrammable bit to enable the High Speed RC oscillator.

Analog To Digital Converter

The ASIC includes a 12-bit ADC (4264) with the followingcharacteristics: (i) capability to effect a conversion in less than 1.5msec with running from a 32 kHz clock; (ii) ability to perform fasterconversions when clocked from the high speed RC oscillator; (iii) haveat least 10 bits of accuracy (12 bit±4 counts); (iv) have a referencevoltage input of 1.220V, with a temperature sensitivity of less than 0.2mV/° C. from 20° C. to 40° C.; (v) full scale input ranges of 0 to1.22V, 0 to 1.774V, 0 to 2.44V, and 0-VDDA, wherein the 1.774 and 2.44Vranges have programmable bits to reduce the conversion range to lowervalues to accommodate lower VDDA voltages; (vi) have current consumptionof less than 50 uA from its power supply; (vi) have a converter capableof operating from the 32 kHz clock or the High Speed RC clock; (vii)have a DNL of less than 1 LSB; and (viii) issue an interrupt at the endof a conversion.

As shown in FIGS. 42A and 42B, the ASIC has an analog multiplexer 4268at the input of the ADC 4264, both of which are controllable bysoftware. In a preferred embodiment, at least the following signals areconnected to the multiplexer:

-   -   (i) VDD—Core Voltage and regulator output    -   (ii) VBAT—Battery source    -   (iii) VDDA—Analog supply    -   (iv) RE—Reference Electrode of Sensor    -   (v) COUNTER—Counter Electrode of Sensor    -   (vi) WORK1-WORK5—Working Electrodes of Sensor    -   (vii) Temperature sensor    -   (viii) At least two external pin analog signal inputs    -   (ix) EIS integrator outputs    -   (x) ItoV current converter output.

The ASIC is configured such that the loading of the ADC will not exceed±0.01 nA for the inputs COUNTER, RE, WORK1-WORK5, the temperaturesensor, and any other input that would be adversely affected by loading.The multiplexer includes a divider for any inputs that have highervoltage than the input voltage range of the ADC, and a buffer amplifierthat will decrease the input resistance of the divided inputs to lessthan 1 nA for load sensitive inputs. The buffer amplifier, in turn, hasa common mode input range from at least 0.8V to VDDA voltage, and anoffset less than 3 mV from the input range from 0.8V to VDDA−0.1V.

In a preferred embodiment, the ASIC has a mode where the ADCmeasurements are taken in a programmed sequence. Thus, the ASIC includesa programmable sequencer 4266 that supervises the measurement of up to 8input sources for ADC measurements with the following programmableparameters:

-   -   (i) ADC MUX input    -   (ii) ADC range    -   (iii) Delay time before measurement, wherein the delays are        programmable from 0 to 62 msec in 0.488 msec steps    -   (iv) Number of measurements for each input from 0 to 255    -   (v) Number of cycles of measurements: 0-255, wherein the cycle        of measurements refers to repeating the sequence of up to 8        input measurements multiple times (e.g., as an outer loop in a        program)    -   (vi) Delay between cycles of measurement, wherein the delays are        programmable from 0 to 62 msec in 0.488 msec steps.

The sequencer 4266 is configured to start upon receiving an auto-measurestart command, and the measurements may be stored in the ASIC forretrieval over the SPI interface. It is noted that the sequencer timebase is programmable between the 32 kHz clock and the High Speed RCoscillator 4262.

Sensor Diagnostics

As was previously described in detail, embodiments of the invention aredirected to use of impedance and impedance-related parameters in, e.g.,sensor diagnostic procedures and Isig/SG fusion algorithms. To that end,in preferred embodiments, the ASIC described herein has the capabilityof measuring the impedance magnitude and phase angle of any WORK sensorelectrode to the RE and COUNTER electrode when in the potentiostatconfiguration. This is done, e.g., by measuring the amplitude and phaseof the current waveform in response to a sine-like waveform superimposedon the WORK electrode voltage. See, e.g., Diagnostic Circuitry 4255 inFIG. 42B.

The ASIC has the capability of measuring the resistive and capacitivecomponents of any electrode to any electrode via, e.g., the ElectrodeMultiplexer 4250. It is noted that such measurements may interfere withthe sensor equilibrium and may require settling time or sensorinitialization to record stable electrode currents. As discussedpreviously, although the ASIC may be used for impedance measurementsacross a wide spectrum of frequencies, for purposes of the embodimentsof the invention, a relatively narrower frequency range may be used.Specifically, the ASIC's sine wave measurement capability may includetest frequencies from about 0.10 Hz to about 8192 Hz. In making suchmeasurements, the minimum frequency resolution in accordance with anembodiment of the invention may be limited as shown in Table 2 below:

TABLE 2 Frequency Min step [Hz] [Hz]  .1 to 15 <1 16 to 31 1 32 to 63 2 64 to 127 4 128 to 255 8 256 to 511 16  512 to 1023 32 1024 to 2047 642048 to 4095 128 4096 to 8192 256

The sinewave amplitude is programmable from at least 10 mVp-p to 50mVp-p in 5 mV steps, and from 60 mVp-p to 100 mVp-p in 10 mV steps. In apreferred embodiment, the amplitude accuracy is better than ±5% or ±5mV, whichever is larger. In addition, the ASIC may measure the electrodeimpedance with accuracies specified in Table 3 below:

TABLE 3 Impedance Phase Measurement Measurement Frequency RangeImpedance Range Accuracy Accuracy .1-10 Hz 2k to 1 MegΩ ±5% ±0.5° 10-100Hz 1k to 100 kΩ ±5% ±0.5° 100 to 8000 Hz .5k to 20 kΩ ±5% ±1.0°

In an embodiment of the invention, the ASIC can measure the inputwaveform phase relative to a time base, which can be used in theimpedance calculations to increase the accuracy. The ASIC may also haveon-chip resistors to calibrate the above electrode impedance circuit.The on-chip resistors, in turn, may be calibrated by comparing them tothe known 1 MegOhm off-chip precision resistor.

Data sampling of the waveforms may also be used to determine theimpedances. The data may be transmitted to an external microprocessorwith the serial peripheral interface (SPI) for calculation andprocessing. The converted current data is sufficiently buffered to beable to transfer 2000 ADC conversions of data to an external devicethrough the SPI interface without losing data. This assumes a latencytime of 8 msec maximum for servicing a data transfer request interrupt.

In embodiments of the invention, rather than, or in addition to,measuring electrode impedance with a sine wave, the ASIC may measureelectrode current with a step input. Here, the ASIC can supplyprogrammable amplitude steps from 10 to 200 mV with better than 5 mVresolution to an electrode and sample (measure) the resulting currentwaveform. The duration of the sampling may be programmable to at least 2seconds in 0.25 second steps, and the sampling interval for measuringcurrent may include at least five programmable binary weighted stepsapproximately 0.5 msec to 8 msec.

The resolution of the electrode voltage samples is smaller than 1 mVwith a range up to ±0.25 volts. This measurement can be with respect toa suitable stable voltage in order to reduce the required dynamic rangeof the data conversion. Similarly, the resolution of the electrodecurrent samples is smaller than 0.04 uA with a range up to 20 uA. Thecurrent measurements can be unipolar if the measurement polarity isprogrammable.

In embodiments of the invention, the current measurement may use anI-to-V converter. Moreover, the ASIC may have on-chip resistors tocalibrate the current measurement. The on-chip resistors, in turn, maybe calibrated by comparing them to the known 1 MegOhm off-chip precisionresistor. The current measurement sample accuracy is better than ±3% or±10 nA, whichever is greater. As before, the converted current data issufficiently buffered to be able to transfer 2000 ADC conversions ofdata to an external device through the SPI interface without losingdata. This assumes a latency time of 8 msec maximum for servicing a datatransfer request interrupt.

Calibration Voltage

The ASIC includes a precision voltage reference to calibrate the ADC.The output voltage is 1.000V±3% with less than ±1.5% variation inproduction, and stability is better than 3 mV over a temperature rangeof 20° C. to 40° C. This precision calibration voltage may becalibrated, via the on-chip ADC, by comparing it to an externalprecision voltage during manufacture. In manufacturing, a calibrationfactor may be stored in a system non-volatile memory (not on this ASIC)to achieve higher accuracy.

The current drain of the calibration voltage circuit is preferably lessthan 25 uA. Moreover, the calibration voltage circuit is able to powerdown to less than 10 nA to conserve battery power when not in use.

Temperature Sensor

The ASIC has a temperature transducer having a sensitivity between 9 and11 mV per degree Celsius between the range −10° C. to 60° C. The outputvoltage of the Temperature Sensor is such that the ADC can measure thetemperature-related voltage with the 0 to 1.22V ADC input range. Thecurrent drain of the Temperature Sensor is preferably less than 25 uA,and the Temperature Sensor can power down to less than 10 nA to conservebattery power when not in use.

VDD Voltage Regulator

The ASIC has a VDD voltage regulator with the following characteristics:

-   -   (i) Minimum input Voltage Range: 2.0V-4.5V.    -   (ii) Minimum output Voltage: 1.6-2.5V±5%, with a default of        2.0V.    -   (iii) Dropout voltage: Vin−Vout<0.15V at Iload=100 uA, Vin=2.0V.    -   (iv) The output voltage is programmable, with an accuracy within        2% of the indicated value per Table 4 below:

TABLE 4 Hex vout hex vout 0 1.427 10 1.964 1 1.460 11 1.998 2 1.494 122.032 3 1.528 13 2.065 4 1.561 14 2.099 5 1.595 15 2.132 6 1.628 162.166 7 1.662 17 2.200 8 1.696 18 2.233 9 1.729 19 2.267 A 1.763 1A2.300 B 1.796 1B 2.334 C 1.830 1C 2.368 D 1.864 1D 2.401 E 1.897 1E2.435 F 1.931 1F 2.468

-   -   (v) The regulator can supply output of 1 mA at 2.5V with an        input voltage of 2.8V.    -   (vi) The regulator also has input and output pads that may be        open circuited if an external regulator is used. The current        draw of the regulator circuit is preferably less than 100 nA in        this non-operational mode.    -   (vii) The change of output voltage from a load of 10 uA to 1 mA        is preferably less than 25 mV.    -   (viii) Current Drain excluding output current @ 1 mA load is        less than 100 uA from source.    -   (ix) Current Drain excluding output current @ 0.1 mA load is        less than 10 uA from source.    -   (x) Current Drain excluding output current @ 10 uA load is less        than 1 uA from source.

General Purpose Comparators

The ASIC includes at least two comparators 4270, 4271 powered from VDDA.The comparators use 1.22V as a reference to generate the threshold. Theoutput of the comparators can be read by the processor and will create amaskable interrupt on the rising or falling edge determined byconfiguration registers.

The comparators have power control to reduce power when not in use, andthe current supply is less than 50 nA per comparator. The response timeof the comparator is preferably less than 50 usec for a 20 mV overdrivesignal, and the offset voltage is less than ±8 mV.

The comparators also have programmable hysteresis, wherein thehysteresis options include threshold=1.22V+Vhyst on a rising input,threshold=1.22−Vhyst on a falling input, or no hysteresis (Vhyst=25±10mV). The output from either comparator is available to any GPIO on anypower plane. (See GPIO section).

Sensor Connection Sensing Circuitry on RE

An analog switched capacitor circuit monitors the impedance of the REconnection to determine if the sensor is connected. Specifically, acapacitor of about 20 pF is switched at a frequency of 16 Hz driven byan inverter with an output swing from VSS to VDD. Comparators will sensethe voltage swing on the RE pad and, if the swing is less than athreshold, the comparator output will indicate a connection. Theabove-mentioned comparisons are made on both transitions of the pulse. Aswing below threshold on both transitions is required to indicate aconnect, and a comparison indicating high swing on either phase willindicate a disconnect. The connect signal/disconnect signal is debouncedsuch that a transition of its state requires a stable indication to thenew state for at least ½ second.

The circuit has six thresholds defined by the following resistances inparallel with a 20 pF capacitor: 500 k, 1 Meg, 2 MEG, 4 Meg, 8 Meg, and16 Meg ohms. This parallel equivalent circuit is between the RE pad anda virtual ground that can be at any voltage between the power rails. Thethreshold accuracy is better than ±30%.

The output of the Sensor Connect sensing circuitry is able toprogrammably generate an interrupt or processor startup if a sensor isconnected or disconnected. This circuit is active whenever the nPOR2_INis high and the VDD and VDDA are present. The current drain for thiscircuit is less than 100 nA average.

WAKEUP Pad

The WAKEUP circuitry is powered by the VDD supply, with an input havinga range from 0V to VBAT. The WAKEUP pad 4272 has a weak pulldown of80±40 nA. This current can be derived from an output of the BIAS_GEN4220. The average current consumed by the circuit is less than 50 nAwith 0 v input.

The WAKEUP input has a rising input voltage threshold, Vih, of 1.22±0.1V, and the falling input threshold is −25 mV±12 mV that of the risingthreshold. In preferred embodiments, the circuit associated with theWAKEUP input draws no more than 100 nA for any input whose value is from−0.2 to VBAT voltage (this current excludes the input pulldown current).The WAKEUP pad is debounced for at least ½ second.

The output of the WAKEUP circuit is able to programmably generate aninterrupt or processor startup if the WAKEUP pad changes state. (See theEvent Handler section). It is important to note that the WAKEUP padcircuitry is configured to assume a low current, <1 nA, if the BatteryProtection Circuit indicates a low battery state.

UART WAKEUP

The ASIC is configured to monitor the nRX_EXT pad 4274. If the nRX_EXTlevel is continuously high (UART BREAK) for longer than ½ second, a UARTWAKEUP event will be generated. The due to sampling the UART WAKEUPevent could be generated with a continuous high as short as ¼ second.The UART WAKEUP event can programmably generate an interrupt, WAKEUPand/or a microprocessor reset (nRESET_OD). (See the Event Handlersection).

In preferred embodiments, the circuit associated with the UART WAKEUPinput draws no more than 100 nA, and the UART WAKEUP pad circuitry isconfigured to assume a low current, <1 nA, if the Battery Protectioncircuitry indicates a Battery Low state. The UART Wakeup input has arising input voltage threshold, Vih, of 1.22±0.1 V. The falling inputthreshold is −25 mV±12 mV that of the rising threshold.

Microprocessor Wakeup Control Signals

The ASIC is able to generate signals to help control the powermanagement of a microprocessor. Specifically, the ASIC may generate thefollowing signals:

-   -   (i) nSHUTDN—nSHUTDN may control the power enable of an off chip        VDD regulator. The nSHUTDN pad is on the VBAT power rail.        nSHUTDN shall be low if the Battery Protection circuitry        indicates a Battery Low state, otherwise nSHUTDN shall be high.    -   (ii) VPAD_EN—VPAD_EN may control the power enable of an external        regulator that supplies VPAD power. An internal signal that        corresponds to this external signal ensures that inputs from the        VPAD pads will not cause extra current due to floating inputs        when the VPAD power is disabled. The VPAD_EN pad is an output on        the VBAT power rail. The VPAD_EN signal is low if the Battery        Protection signal indicates a low battery. The VPAD_EN signal        may be set low by a software command that starts a timer; the        terminal count of the timer forces VPAD_EN low. The following        events may cause the VPAD_EN signal to go high if the Battery        Protection signal indicates a good battery (see Event Handler        for more details): nPOR2_IN transitioning from low to high;        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high, and/or high to low, (programmable); UART Break; and RTC        Time Event (programmable).    -   (iii) UP_WAKEUP—UP_WAKEUP may connect to a microprocessor wakeup        pad. It is intended to wakeup the microprocessor from a sleep        mode or similar power down mode. The UP_WAKEUP pad is an output        on the VPAD power rail. The UP_WAKEUP signal can be programmed        to be active low, active high or a pulse. The UP_WAKEUP signal        may be set low by a software command that starts a timer; the        terminal count of the timer forces UP_WAKEUP low. The following        events may cause the UP_WAKEUP signal to go high if the Battery        Protection signal indicates a good battery (see Event Handler        for more details): nPOR2_IN transitioning from low to high;        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high, and/or high to low, (programmable); UART Break; and RTC        Time Event (programmable). The WAKEUP signal may be delayed by a        programmable amount. If WAKEUP is programmed to be a pulse, the        pulse width may be programmed.    -   (iv) CLK_32 KHZ—CLK_32 KHZ pad may connect to a microprocessor        to supply a low speed clock. The clock is on-off programmable        and programmably turns on to wakeup events. The CLK_32 KHZ pad        is an output on the VPAD power rail. The CLK_32 KHZ signal is        low if the Battery Protection signal indicates a low battery.        The CLK_32 KHZ output may be programmed off by a programmable        bit. The default is ON. The CLK_32 KHZ signal may be disabled by        a software command that starts a timer; The terminal count of        the timer forces CLK_32 KHZ low. The following events may cause        the CLK_32 KHZ signal to be enabled if the Battery Protection        signal indicates a good battery (see Event Handler for more        details): nPOR2_IN transitioning from low to high; SW/Timer        (programmable); WAKEUP transition; low to high, and/or high to        low, (programmable); Sensor Connect transition; low to high,        and/or high to low, (programmable); UART Break; RTC Time Event        (programmable); and Detection of low battery by Battery        Protection Circuit.    -   (v) nRESET_OD—nRESET_OD may connect to a microprocessor to cause        a microprocessor reset. The nRESET_OD is programmable to wakeup        events. The nRESET_OD pad is an output on the VPAD power rail.        This pad is open drain (nfet output). The nRESET_OD signal is        low if the Battery Protection signal indicates a low battery.        The nRESET_OD active time is programmable from 1 to 200 msec.        The default is 200 ms. The following events may cause the        nRESET_OD signal to be asserted low (see Event Handler for more        details): nPOR2_IN; SW/Timer (programmable); WAKEUP transition;        low to high, and/or high to low, (programmable); Sensor Connect        transition; low to high, and/or high to low, (programmable);        UART Break; and RTC Time Event (programmable).    -   (vi) UP_INT—UP_INT may connect to a microprocessor to        communicate interrupts. The UP_INT is programmable to wakeup        events. The UP_INT pad is an output on the VPAD power rail. The        UP_INT signal is low if the Battery Protection signal indicates        a low battery. The UP_INT signal may be set high by a software        command that starts a timer; the terminal count of the timer        forces UP_INT high. The following events may cause the UP_INT        signal to be asserted high if the Battery Protection signal        indicates a good battery (see Event Handler for more details):        SW/Timer (programmable); WAKEUP transition; low to high, and/or        high to low, (programmable); Sensor Connect transition; low to        high and/or high to low, (programmable); UART Break; RTC Time        Event (programmable); Detection of low battery by Battery        Protection Circuit; and any of the ASIC interrupts when        unmasked.

The ASIC has GPIO1 and GPIO0 pads able to act as boot mode control for amicroprocessor. A POR2 event will reset a 2 bit counter whose bits mapto GPIO1 & GPIO0 (MSB, LSB respectively). A rising edge of UART breakincrements the counter by one, wherein the counter counts by modulo 4,and goes to zero if it is incremented in state 11. The boot mode counteris pre-settable via SPI.

Event Handler/Watchdog

The ASIC incorporates an event handler to define the responses toevents, including changes in system states and input signals. Eventsinclude all sources of interrupts (e.g. UART_BRK, WAKE_UP, SensorConnect, etc. . . . ). The event handler responses to stimuli areprogrammable by the software through the SPI interface. Some responses,however, may be hardwired (non-programmable).

The event handler actions include enable/disable VPAD_EN, enable/disableCLK_32 KHZ, assert nRESET_OD, assert UP_WAKEUP, and assert UP_INT. TheEvent Watchdog Timer 1 through Timer 5 are individually programmable in250 msec increments from 250 msec to 16,384 seconds. The timeouts forEvent Watchdog timers 6 through 8 are hardcoded. The timeout for Timer6and Timer7 are 1 minute; timeout for Timer8 is 5 minutes.

The ASIC also has a watchdog function to monitor the microprocessor'sresponses when triggered by an event. The event watchdog is activatedwhen the microprocessor fails to acknowledge the event inducedactivities. The event watchdog, once activated, performs a programmablesequence of actions, Event Watchdog Timer 1-5, and followed by ahard-wired sequence of actions, Event Watchdog Timer 6-8, to re-gain theresponse of the microprocessor. The sequence of actions includesinterrupt, reset, wake up, assert 32 KHz clock, power down and power upto the microprocessor.

During the sequences of actions, if the microprocessor regains itsability to acknowledge the activities that had been recorded, the eventwatchdog is reset. If the ASIC fails to obtain an acknowledgement fromthe microprocessor, the event watchdog powers down the microprocessor ina condition that will allow UART_BRK to reboot the microprocessor and itwill activate the alarm. When activated, the alarm condition generates asquare wave with a frequency of approximately 1 kHz on the pad ALARMwith a programmable repeating pattern. The programmable pattern has twoprogrammable sequences with programmable burst on and off times. Thealarm has another programmable pattern that may be programmed via theSPI port. It will have two programmable sequences with programmableburst on and off times.

Digital to Analog (D/A)

In a preferred embodiment, the ASIC has two 8 bit D/A converters 4276,4278 with the following characteristics:

-   -   (i) The D/A settles in less than 1 msec with less than 50 pF        load.    -   (ii) The D/A has at least 8 bits of accuracy.    -   (iii) The output range is programmable to either 0 to 1.22V or 0        to VDDA.    -   (iv) Temperature sensitivity of the D/A voltage reference is        less than 1 mV/° C.    -   (v) The DNL is less than 1 LSB.    -   (vi) Current consumed by the D/A is less than 2 uA from the VDDA        supply.    -   (vii) Each D/A has an output 1 to a pad.    -   (viii) The D/A outputs are high impedance. Loading current must        be less than 1 nA.    -   (ix) The D/A pads can be programmed to output a digital signal        from a register. The output swing is from VSSA to VDDA.

Charger/Data Downloader Interface

The TX_EXT_OD 4280 is an open drain output whose input is the signal onthe TX UP input pad. This will allow the TX_EXT_OD pad to be open in theUART idle condition. The TX_EXT_OD pad has a comparator monitoring itsvoltage. If the voltage is above the comparator threshold voltage for adebounce period (¼ second), the output, nBAT_CHRG_EN (4281), will golow. This comparator and other associated circuitry with this functionare on the VBAT and/or VDDBU planes.

The circuitry associated with this function must allow lows on TX_EXT_ODpad that result from normal communication with an external devicewithout disabling the assertion of nBAT_CHRG_EN. If POR1 is active,nBAT_CHRG_EN will be high (not asserted). The comparator's thresholdvoltage is between 0.50V and 1.2V. The comparator will have hysteresis;The falling threshold is approximately 25 mV lower than the risingthreshold.

The nRX_EXT pad inverts the signal on this pad and output it to RX UP.In this way, the nRX_EXT signal will idle low. The nRX_EXT must acceptinputs up to VBAT voltage. The nRX_EXT threshold is 1.22V±3%. The outputof this comparator will be available over the SPI bus for amicroprocessor to read.

The nRX_EXT pad also incorporates a means to programmably source acurrent, which will be 80±30 nA, with the maximum voltage being VBAT.The ASIC layout has mask programmable options to adjust this currentfrom 30 nA to 200 nA in less than 50 nA steps with a minimal number ofmask layer changes. A programmable bit will be available to block theUART break detection and force the RX UP high. In normal operation, thisbit will be set high before enabling the current sourcing to nRX_EXT andthen set low after the current sourcing is disabled to ensure that noglitches are generated on RX UP or that a UART break event is generated.Note to implement a wet connector detector, while the current sourceinto nRX_EXT is active, an RX comparator output indicating a low inputvoltage would indicate leakage current. The ASIC includes a pulldownresistor approximately 100 k ohms on the nRX_EXT pad. This pulldown willbe disconnected when the current source is active.

Sensor Connect Switch

The ASIC shall have a pad, SEN_CONN_SW (4282), which is able to detect alow resistance to VSS (4284). The SEN_CONN_SW sources a current from 5to 25 uA with SEN_CONN_SW=0V and has a maximum open circuit voltage of0.4V. The ASIC layout has mask programmable options to adjust thiscurrent from 1 uA to 20 uA in less than 5 uA steps with a minimal numberof mask layer changes. The SEN_CONN_SW has associated circuitry thatdetects the presence of a resistance between SEN_CONN_SW and VSSA (4234)whose threshold is between 2 k and 15 k ohms. The average current drainof this circuit is 50 nA max. Sampling must be used to achieve this lowcurrent.

Oscillator Calibration Circuit

The ASIC has counters whose inputs can be steered to internal orexternal clock sources. One counter generates a programmable gatinginterval for the other counter. The gating intervals include 1 to 15seconds from the 32 kHz oscillator. The clocks that can be steered toeither counter are 32 kHz, RC oscillator, High Speed RC oscillator, andan input from any GPIO pad.

Oscillator Bypassing

The ASIC can substitute external clocks for each of the oscillators'outputs. The ASIC has a register that can be written only when aspecific TEST_MODE is asserted. This register has bits to enable theexternal input for the RC Oscillator, and may be shared with otheranalog test control signals. However, this register will not allow anyoscillator bypass bits to be active if the TEST_MODE is not active.

The ASIC also has an input pad for an external clock to bypass the RCOscillator. The pad, GPIO_VBAT, is on the VBAT power plane. The ASICfurther includes a bypass enable pad for the 32 KHZ oscillator,OSC32K_BYPASS. When high, the 32 KHZ oscillator output is supplied bydriving the OSC32 KHZ_IN pad. It is noted that, normally, the OSC32KHZ_IN pad is connected to a crystal.

The ASIC has inputs for an external clock to bypass the HS_RC_OSC. Thebypass is enabled by a programmable register bit. The HS_RC_OSC may besupplied programmably by either the GPIO on the VDD plane or by GPIOs onthe VPAD plane.

SPI Slave Port

The SPI slave port includes an interface consisting of a chip selectinput (SPI_nCS) 4289, a clock input (SPI_CK) 4286, a serial data input(SPI_MOSI) 4287, and a serial data output (SPI_MISO) 4288. The chipselect input (SPI_nCS) is an active low input, asserted by an off-chipSPI master to initiate and qualify an SPI transaction. When SPI_nCS isasserted low, the SPI slave port configures itself as a SPI slave andperforms data transactions based on the clock input (SPI_CK). WhenSPI_nCS is inactive, the SPI slave port resets itself and remains inreset mode. As this SPI interface supports block transfers, the mastershould keep SPI_nCS low until the end of a transfer.

The SPI clock input (SPI_CK) will always be asserted by the SPI master.The SPI slave port latches the incoming data on the SPI_MOSI input usingthe rising edge of SPI_CK and driving the outgoing data on the SPI_MISOoutput using the falling edge of SPI_CK. The serial data input(SPI_MOSI) is used to transfer data from the SPI master to the SPIslave. All data bits are asserted following the falling edge of SPI_CK.The serial data output (SPI_MISO) is used to transfer data from the SPIslave to the SPI master. All data bits are asserted following thefalling edge of SPI_CK.

SPI_nCS, SPI_CK and SPI_MOSI are always driven by the SPI master, unlessthe SPI master is powered down. If VPAD_EN is low, these inputs areconditioned so that the current drain associated with these inputs isless than 10 nA and the SPI circuitry is held reset or inactive.SPI_MISO is only driven by the SPI slave port when SPI_nCS is active,otherwise, SPI_MISO is tri-stated.

The chip select (SPI_nCS) defines and frames the data transfer packet ofan SPI data transaction. The data transfer packet consists of threeparts. There is a 4-bit command section followed by a 12-bit addresssection, which is then followed by any number of 8 bit data bytes. Thecommand bit 3 is used as the direction bit. A “1” indicates a writeoperation, and a “0” indicates a read operation. The combinations ofcommand bit 2, 1 and 0 have the following definitions. Unusedcombinations are undefined.

-   -   (i) 0000: read data and increment address.    -   (ii) 0001: read data, no change to address    -   (iii) 0010: read data, decrement address    -   (iv) 1000: write data and increment address    -   (v) 1001: write data, no change to address    -   (vi) 1010: write data, decrement address    -   (vii) x011: Test Port Addressing

The 12-bit address section defines the starting byte address. If SPI_nCSstays active after the first data byte, to indicate a multi-bytetransfer, the address is incremented by one after each byte istransferred. Bit<11> of the address (of address<11:0>) indicates thehighest address bit. The address wraps around after reaching theboundary.

Data is in the byte format, and a block transfer can be performed byextending SPI_nCS to allow all bytes to be transferred in one packet.

Microprocessor Interrupt

The ASIC has an output at the VPAD logic level, UP_INT, for the purposeof sending interrupts to a host microprocessor. The microprocessorinterrupt module consists of an interrupt status register, an interruptmask register, and a function to logically OR all interrupt statusesinto one microprocessor interrupt. The interrupt is implemented tosupport both edge sensitive and level sensitive styles. The polarity ofthe interrupt is programmable. The default interrupt polarity is TBD.

In a preferred embodiment, all interrupt sources on the AFE ASIC will berecorded in the interrupt status register. Writing a “1” to thecorresponding interrupt status bit clears the corresponding pendinginterrupt. All interrupt sources on the AFE ASIC are mask-able throughthe interrupt mask register. Writing a “1” to the correspondinginterrupt mask bit enables the masking of the corresponding pendinginterrupt. Writing a “0” to the corresponding interrupt mask bitdisables the masking of the corresponding interrupt. The default stateof the interrupt mask register is TBD.

General Purpose Input/Outputs (GPIOs)/Parallel Test Port

In embodiments of the invention, the ASIC may have eight GPIOs thatoperate on VPAD level signals. The ASIC has one GPIO that operates on aVBAT level signal, and one GPIO that operates on a VDD level signal. Alloff the GPIOs have at least the following characteristics:

-   -   (i) Register bits control the selection and direction of each        GPIO.    -   (ii) The ASIC has a means to configure the GPIOs as inputs that        can be read over the SPI interface.    -   (iii) The ASIC has a means to configure the GPIOs as input to        generate an interrupt.    -   (iv) The ASIC has a means to configure each GPIO as an output to        be controlled by a register bit that can be written over the SPI        interface.    -   (v) Programmably, the ASIC is able to output an input signal        applied to GPIO_VBAT or GPIO_VDD to a GPIO (on the VPAD power        plane). (Level shifting function).    -   (vi) The ASIC has a means to configure each GPIO as an input to        the oscillator calibration circuit.    -   (vii) The ASIC has a means to configure each general purpose        comparator output to at least one GPIO on each power plane. The        polarity of the comparator output is programmable by a        programmable bit.    -   (viii) The GPIOs have microprocessor interrupt generating        capability.    -   (ix) The GPIOs are programmable to open drain outputs.    -   (x) The GPIOs on the VPAD power plane are configurable to        implement boot control of a microprocessor.

A Parallel Test Port shares the 8-bit GPIOs on the VPAD voltage plane.The test port will be used for observing register contents and variousinternal signals. The outputs of this port are controlled by the portconfiguration register in the normal mode. Writing 8′hFF to bothGPIO_O1S_REG & GPIO_O2S_REG registers will steer the test port data onthe GPIO outputs, while writing 8′h00 to the GPIO_ON_REG register willdisable the test port data and enable the GPIO data onto the GPIOoutputs.

Registers and pre-grouped internal signals can be observed over thistest port by addressing the target register through the SPI slave port.The SPI packet has the command bits set to 4′b0011 followed by the12-bit target register address. The parallel test port continues todisplay the content of the addressed register until the next Test PortAddressing command is received.

Analog Test Ports

The IC has a multiplexer feeding the pad, TP_ANAMUX (4290), which willgive visibility to internal analog circuit nodes for testing. The ICalso has a multiplexer feeding the pad, TP_RES (4260), which will givevisibility to internal analog circuit nodes for testing. This pad willalso accommodate a precision 1 meg resistor in usual application toperform various system calibrations.

Chip ID

The ASIC includes a 32 bit mask programmable ID. A microprocessor usingthe SPI interface will be able to read this ID. This ID is to be placedin the analog electronics block so that changing the ID does not requirea chip reroute. The design should be such that only one metal or onecontact mask change is required to change the ID.

Spare Test Outputs

The ASIC has 16 spare digital output signals that can be multiplexed tothe 8 bit GPIO under commands sent over the SPI interface. These signalswill be organized as two 8 bit bytes, and will be connected to VSS ifnot used.

Digital Testing

The ASIC has a test mode controller that uses two input pins, TEST_CTL0(4291) and TEST_CTL1 (4292). The test controller generates signals fromthe combination of the test control signals that have the followingfunctionality (TEST_CTL<1:0>):

-   -   (i) 0 is normal operating mode;    -   (ii) 1 is Analog Test Mode;    -   (iii) 2 is Scan Mode;    -   (iv) 3 is Analog Test mode with the VDD_EN controlled by an        input to GPIO_VBAT.

The test controller logic is split between the VDD and VDDBU powerplanes. During scan mode, testing LT_VBAT should be asserted high tocondition the analog outputs to the digital logic. The ASIC has a scanchain implemented in as much digital logic as reasonably possible forfast digital testing.

Leakage Test Pin

The ASIC has a pin called LT_VBAT that, when high, will put all theanalog blocks into an inactive mode so that only leakage currents willbe drawn from the supplies. LT_VBAT causes all digital outputs fromanalog blocks to be in a stable high or low state as to not affectinterface logic current drain. The LT_VBAT pad is on the VBAT plane witha pulldown with a resistance between 10 k and 40 k ohms.

Power Requirements

In embodiments of the invention, the ASIC includes a low power modewhere, at a minimum, the microprocessor clock is off, the 32 kHz realtime clock runs, and circuitry is active to detect a sensor connection,a change of level of the WAKE_UP pin, or a BREAK on the nRX_EXT input.This mode has a total current drain from VBAT (VDDBU), VDD, and VDDA of4.0 uA maximum. When the Battery Protection Circuit detects a lowbattery (see Battery Protection Circuit description), the ASIC goes to amode with only the VBAT and VDDBU power planes active. This is calledLow Battery state. The VBAT current in this mode is less than 0.3 uA.

With the ASIC programmed to the potentiostat configuration with any oneWORK electrode active in the H2O2 (peroxide) mode with its voltage setto 1.535V, the COUNTER amplifier on with the VSET_RE set to 1.00V, a 20MEG load resistor connected between WORK and the COUNTER, the COUNTERand RE connected together and assuming one WORK electrode currentmeasurement per minute, the average current drain of all power suppliesis less than 7 uA. The measured current after calibration should be26.75 nA±3%. Enabling additional WORK electrodes increases the combinedcurrent drain by less than 2 uA with the WORK electrode current of 25nA.

With the ASIC programmed to the potentiostat configuration with thediagnostic function enabled to measure the impedance of one of the WORKelectrodes with respect to the COUNTER electrode, the ASIC is configuredto meet the following:

-   -   (i) Test frequencies: 0.1, 0.2, 0.3, 0.5 Hz, 1.0, 2.0, 5.0, 10,        100, 1000 and 4000 Hz.    -   (ii) The measurement of the above frequencies is not to exceed        50 seconds.    -   (iii) The total charge supplied to the ASIC is less than 8        millicoulombs.

Environment

In preferred embodiments of the invention, the ASIC:

-   -   (i) Operates and meets all specifications in the commercial        temperature range of 0 to 70° C.    -   (ii) Functionally operates between −20° C. and 80° C., but may        do so with reduced accuracy.    -   (iii) Is expected to operate after being stored in a temperature        range of −30 to 80° C.    -   (iv) Is expected to operate in the relative humidity range of 1%        to 95%.    -   (v) ESD protection is greater than ±2 KV, Human Body Model on        all pins when packaged in a TBD package, unless otherwise        specified.    -   (vi) Is configured such that the WORK1-WORK5, COUNTER, RE,        TX_EXT_OD, and nRX_EXT pads withstand greater than ±4 KV Human        Body Model.    -   (vii) Is configured such that the leakage current of the        WORK1-WORK5 and RE pads is less than 0.05 nA at 40° C.

In embodiments of the invention, the ASIC may be fabricated in 0.25micron CMOS process, and backup data for the ASIC is on DVD disk,916-TBD.

As described in detail hereinabove, the ASIC provides the necessaryanalog electronics to: (i) support multiple potentiostats and interfacewith multi-terminal glucose sensors based on either Oxygen or Peroxide;(ii) interface with a microcontroller so as to form a micropower sensorsystem; and (iii) implement EIS diagnostics based on measurement ofEIS-based parameters. The measurement and calculation of EIS-basedparameters will now be described in accordance with embodiments of theinventions herein.

As mentioned previously, the impedance at frequencies in the range from0.1 Hz to 8 kHz can provide information as to the state of the sensorelectrodes. The AFE IC circuitry incorporates circuitry to generate themeasurement forcing signals and circuitry to make measurements used tocalculate the impedances. The design considerations for this circuitryinclude current drain, accuracy, speed of measurement, the amount ofprocessing required, and the amount of on time required by a controlmicroprocessor.

In a preferred embodiment of the invention, the technique the AFE ICuses to measure the impedance of an electrode is to superimpose a sinewave voltage on the dc voltage driving an electrode and to measure thephase and amplitude of the resultant AC current. To generate the sinewave, the AFE IC incorporates a digitally-synthesized sine wave current.This digital technique is used because the frequency and phase can beprecisely controlled by a crystal derived timebase and it can easilygenerate frequencies from DC up to 8 kHz. The sine wave current isimpressed across a resistor in series with a voltage source in order toadd the AC component to the electrode voltage. This voltage is the ACforcing voltage. It is then buffered by an amplifier that drives aselected sensor electrode.

The current driving the electrode contains the resultant AC currentcomponent from the forcing sine wave and is converted to a voltage. Thisvoltage is then processed by multiplying it by a square wave that has afixed phase relative to the synthesized sine wave. This multipliedvoltage is then integrated. After the end of a programmable number ofintegration intervals—an interval being an integral number of ½ periodsof the driving sine wave—the voltage is measured by the ADC. Bycalculations involving the values of the integrated voltages, the realand imaginary parts of the impedance can be obtained.

The advantage of using integrators for the impedance measurement is thatthe noise bandwidth of the measurement is reduced significantly withrespect to merely sampling the waveforms. Also, the sampling timerequirements are significantly reduced which relaxes the speedrequirement of the ADC.

FIG. 45 shows the main blocks of the EIS circuitry in the AFE IC(designated by reference numeral 4255 in FIG. 42B). The IDAC 4510generates a stepwise sine wave in synchrony with a system clock. A highfrequency of this system clock steps the IDAC through the lookup tablethat contains digital code. This code drives the IDAC, which generatesan output current approximating a sine wave. This sine wave current isforced across a resistor to give the AC component, Vin_ac, with the DCoffset, VSET8 (4520). When the IDAC circuit is disabled, the DC outputvoltage reverts to VSET8, so the disturbance to the electrodeequilibrium is minimized. This voltage is then buffered by an amplifier4530 that drives the electrode through a resistor in series, Rsense. Thedifferential voltage across Rsense is proportional to the current. Thisvoltage is presented to a multiplier 4540 that multiplies the voltage byeither +1 or −1. This is done with switches and a differential amplifier(instrumentation amplifier). The system clock is divided to generate thephase clock 4550 which controls the multiply function and can be set to0, 90, 180 or 270 degrees relative to the sine wave.

The plots in FIGS. 46A-46F and 47A-47F show a simulation of the signalsof the circuit shown in FIG. 45 to a current that has 0 degree phaseshift, which represents a real resistance. For these examplesimulations, the simulation input values were selected to give thecurrent sense voltage equal to 0.150V. To obtain enough information toderive the impedance and phase, two integrations are required: one witha 0 degree phase multiply (FIGS. 46A-46F) and one with a 90 degree phasemultiply (FIGS. 47A-47F).

Calculation of Impedance

The equations describing the integrator output are provided below. Forsimplicity, only ½ of a sine wave period is considered. As can be seenfrom the plots of FIGS. 46A-46F and 47A-47F, total integrator outputwill be approximately the integrated value of a ½ sine wave cyclemultiplied by the number of ½ cycles integrated. It is noted that themultiplying switches in relation with the integrate time perform a“gating” function of the signal to the integrator; this can be viewed assetting the limits of integration. The multiplying signal has a fixedphase to the generated sine wave. This can be set to 0, 90, 180, or 270degrees with software. If the sine wave is in phase (0 degree shift)with respect to the multiply square wave, the limits of integration willbe π (180°) and 0 (0°). If the sine wave is shifted by 90 degrees, thelimits of integration can be viewed as ¾π (270°) and ¼π (90°).

The formulas with the multiplying square wave in-phase (0°) with respectto the driving sine wave are shown below. This will yield a voltage thatis proportional to the real component of the current. It is noted that Φis the phase shift of the sine wave relative to the multiplying squarewave; Vout is the integrator output, and Aamp1 is the current sine waveamplitude. Also the period of the sine wave is 1/f, and RC is the timeconstant of the integrator.

$v_{{out}\; 0} = {{\int_{0}^{\frac{1}{2f}}{\frac{V_{in}}{RC}{\partial t}}} = {{\frac{A_{ampl}}{RC}{\int_{0}^{\frac{1}{2f}}{\sin \left\lbrack {{2\pi \; f{\partial t}} + \varphi} \right\rbrack}}} = {{{{- \frac{A_{ampl}}{2\pi \; {fRC}}}{\cos\left\lbrack {{2\pi \; {ft}} + \varphi} \right\rbrack}}_{0}^{\frac{1}{2f}}\mspace{79mu} v_{{out}\; 0}} = {- {\frac{A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos \left\lbrack {\pi + \varphi} \right\rbrack} - {\cos \lbrack\varphi\rbrack}} \right\rbrack}}}}}$     cos (φ + ϕ) = cos (φ)cos (ϕ) − sin (φ)sin (ϕ);     cos (π + φ) = −cos (φ);      cos (−φ) = cos (φ)$v_{{out}\; 0} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos \left( {\pi + \phi} \right)} - {\cos (\varphi)}} \right\rbrack} = {{\frac{A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos (\varphi)} + {\cos (\varphi)}} \right\rbrack} = {\frac{A_{ampl}}{\pi \; {fRC}}{\cos (\varphi)}}}}$

If Φ=0,

$v_{{out}\; 0} = {\frac{A_{ampl}}{\pi \; {fRC}}.}$

This corresponds to the real part of the current.

For the multiplying square wave quadrature phase (90°) with respect tothe driving sine wave to yield an output proportional to the imaginarycomponent of the current:

$v_{{out}\; 90} = {{\int_{\frac{1}{4f}}^{\frac{3}{4f}}{\frac{V_{in}}{RC}{\partial t}}} = {{\frac{A_{ampl}}{RC}{\int_{\frac{1}{4f}}^{\frac{3}{4f}}{\sin \left\lbrack {{2\pi \; f{\partial t}} + \phi} \right\rbrack}}} = {{{{- \frac{A_{ampl}}{2\pi \; {fRC}}}{\cos \left\lbrack {{2\pi \; {ft}} + \varphi} \right\rbrack}}_{\frac{1}{4f}}^{\frac{3}{4f}}\mspace{79mu} v_{{out}\; 90}} = {- {\frac{A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\cos \left\lbrack {{\frac{3}{2}\pi} + \varphi} \right\rbrack} - {\cos \left\lbrack {{\frac{1}{2}\pi} + \varphi} \right\rbrack}} \right\rbrack}}}}}$

     cos (φ + ϕ) = cos (φ)cos (ϕ) − sin (φ)sin (ϕ);$\mspace{79mu} {{{\cos \left\lbrack {{\frac{3}{2}\pi} + \varphi} \right\rbrack} = {\sin (\varphi)}};}$$\mspace{79mu} {{\cos \left\lbrack {{\frac{1}{2}\pi} + \varphi} \right\rbrack} = {- {\sin (\varphi)}}}$$v_{{out}\; 90} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\sin (\varphi)} + {\sin (\phi)}} \right\rbrack} = {{\frac{- A_{ampl}}{2\pi \; {fRC}}\left\lbrack {{\sin (\varphi)} + {\sin (\varphi)}} \right\rbrack} = {\frac{- A_{ampl}}{\pi \; {fRC}}{\sin (\varphi)}}}}$

If Φ=0,

$v_{{out}\; 90} = {{\frac{A_{ampl}}{RC}{\sin (\varphi)}} = 0.}$

This corresponds to the imaginary part of the current.

In the first example plot shown in FIGS. 46A-46F, A_(amp1) is 0.150 v,the frequency is 1 kHz, Φ=0, the RC for the integrator is 20M ohm and 25pF which gives RC=0.5 msec. Plugging in those numbers into theequations, gives 0.09549 v, which favorably compares to the integratoroutput of the plot in FIG. 46. It is noted that the integrator outputover the period of integration is the delta voltage from the start ofintegration to the measurement.

For the 90° square wave multiply, the result should be 0 since sin(0)=0.The simulation result is close to this value.

To calculate the phase:

since

${\frac{v_{{out}\; 90}}{v_{out}} = \frac{\sin (\varphi)}{\cos (\varphi)}},$

it follows:

$\varphi = {{\arctan \; \frac{\sin (\varphi)}{\cos (\varphi)}} = {\arctan \frac{v_{{out}\; 90}}{v_{out}}}}$

where V_(out90) is the integrator output with the 90° phase shift forthe multiply, and V_(out0) is the integrator output for the 0° phaseshift. The V_(out90) and V_(out0) outputs must be integrated for thesame number of ½ cycles or normalized by the number of cycles. It isimportant to note that, in the actual software (e.g., ASIC)implementation, only integral cycles (360°) are allowed because anintegral number of cycles compensates for any offset in the circuitrybefore the multiplier.

The magnitude of the current can be found from

${I} = \frac{A_{ampl}}{R_{sense}}$ and$A_{ampl} = \frac{v_{{out\_}90}\pi \; {fRC}}{\sin (\varphi)}$ or${A_{ampl} = \frac{v_{{out\_}0}\pi \; {fRC}}{\cos (\varphi)}},{or}$$A_{ampl} = {\pi \; {fRC}{\sqrt{V_{{{out}\_}0}^{2} + V_{{{out}\_}90}^{2}}.}}$

This current has the phase angle as calculated above.

The above analysis shows that one can determine the current amplitudeand its phase with respect to the multiplying signal. The forcingvoltage is generated in a fixed phase (0, 90, 180 or 270 degrees) withrespect to the multiplying signal—this is done digitally so that it isprecisely controlled. But there is at least one amplifier in the pathbefore the forcing sine wave is applied to the electrode; this willintroduce unwanted phase shift and amplitude error. This can becompensated for by integrating the forcing sine wave signal obtainedelectrically near the electrode. Thus, the amplitude and any phase shiftof the forcing voltage can be determined. Since the path for both thecurrent and voltage waveform will be processed by the same circuit, anyanalog circuit gain and phase errors will cancel.

Since the variable of interest is the impedance, it may not be necessaryto actually calculate the A_(amp1). Because the current waveform and thevoltage waveform are integrated through the same path, there exists asimple relationship between the ratio of the current and the voltage.Calling the integrated current sense voltage V_(I) _(_) _(out) and theintegrated electrode voltage as V_(V) _(_) _(out) with the additionalsubscript to describe the phase of the multiplying function:

${I = {{\frac{A_{I\_ ampl}}{R_{sense}}{\angle\varphi}} = {\frac{V_{{I\_ out}\_ 0}\pi \; {fRC}}{{\cos (\varphi)}R_{sense}}{\angle\varphi}}}};$$V = {{A_{V\_ ampl}{\angle\theta}} = {\frac{V_{{V\_ out}\_ 0}\pi \; {fRC}}{\cos (\theta)}{\angle\theta}}}$

The impedance will be the voltage divided by the current. Thus,

$Z = {\frac{{V}{\angle\theta}}{{I}{\angle\varphi}} = {\frac{\frac{V_{{V\_ out}\_ 0}\pi \; {fRC}\; {\angle\theta}}{\cos (\theta)}}{\frac{V_{{I\_ out}\_ 0}\pi \; {fRC}\; {\angle\varphi}}{{\cos (\varphi)}R_{sense}}} = {R_{sense}*\frac{V_{{V\_ out}\_ 0}{\cos (\varphi)}}{V_{{I\_ out}\_ 0}{\cos (\theta)}}{\angle \left( {\theta - \varphi} \right)}}}}$

The magnitudes of the voltage and the current can also be obtained fromthe square root of the squares of the 0 and 90 degree phase integrationvoltages. As such, the following may also be used:

$Z = {\frac{{V}{\angle\theta}}{{I}{\angle\varphi}} = {\frac{\sqrt{V_{{V\_ out}\_ 0}^{2} + V_{{V\_ out}\_ 90}^{2}}{\angle\theta}}{\sqrt{V_{{I\_ out}\_ 0}^{2} + V_{{I\_ out}\_ 90}^{2}}{\angle\varphi}} = {R_{sense}*\frac{\sqrt{V_{{V\_ out}\_ 0}^{2} + V_{{V\_ out}\_ 90}^{2}}}{\sqrt{V_{{I\_ out}\_ 0}^{2} + V_{{I\_ out}\_ 90}^{2}}}{\angle \left( {\theta - \varphi} \right)}}}}$

The integration of the waveforms may be done with one hardwareintegrator for the relatively-higher frequencies, e.g., those aboveabout 256 Hz. The high frequencies require four measurement cycles: (i)one for the in-phase sensor current; (ii) one for the 90 degree out ofphase sensor current; (iii) one for the in-phase forcing voltage; and(iv) one for the 90 degree out of phase forcing voltage.

Two integrators may be used for the relatively-lower frequencies, e.g.,those lower than about 256 Hz, with the integration value consisting ofcombining integrator results numerically in the system microprocessor.Knowing how many integrations there are per cycle allows themicroprocessor to calculate the 0 and 90 degree componentsappropriately.

Synchronizing the integrations with the forcing AC waveform and breakingthe integration into at least four parts at the lower frequencies willeliminate the need for the hardware multiplier as the combining of theintegrated parts in the microprocessor can accomplish the multiplyingfunction. Thus, only one integration pass is necessary for obtaining thereal and imaginary current information. For the lower frequencies, theamplifier phase errors will become smaller, so below a frequency, e.g.,between 1 Hz and 50 Hz, and preferably below about 1 Hz, the forcingvoltage phase will not need to be determined. Also, the amplitude couldbe assumed to be constant for the lower frequencies, such that only onemeasurement cycle after stabilization may be necessary to determine theimpedance.

As noted above, whereas one hardware integrator is used for therelatively-higher frequencies, for the relatively-lower frequencies, twointegrators may be used. In this regard, the schematic in FIG. 45 showsthe EIS circuitry in the AFE IC as used for the relatively-higher EISfrequencies. At these frequencies, the integrator does not saturatewhile integrating over a cycle. In fact, multiple cycles are integratedfor the highest frequencies as this will provide a larger output signalwhich results in a larger signal to noise ratio.

For the relatively-lower frequencies, such as, e.g., those below about500 Hz, the integrator output can saturate with common parameters.Therefore, for these frequencies, two integrators are used that arealternately switched. That is, while a first integrator is integrating,the second integrator is being read by the ADC and then is reset(zeroed) to make it ready to integrate when the integration time forfirst integrator is over. In this way, the signal can be integratedwithout having gaps in the integration. This would add a secondintegrator and associated timing controls to the EIS circuitry shown inFIG. 45.

Stabilization Cycle Considerations

The above analysis is for steady state conditions in which the currentwaveform does not vary from cycle to cycle. This condition is not metimmediately upon application of a sine wave to a resistor-capacitor (RC)network because of the initial state of the capacitor. The current phasestarts out at 0 degrees and progresses to the steady state value.However, it would be desirable for the measurement to consume a minimumamount of time in order to reduce current drain and also to allowadequate time to make DC sensor measurements (Isigs). Thus, there is aneed to determine the number of cycles necessary to obtain sufficientlyaccurate measurements.

The equation for a simple RC circuit—with a resistor and capacitor inseries—is

$v_{ac} = {{R*{I(t)}} + {\frac{1}{C}{\int{{I(t)}{\partial t}}}}}$

Solving the above for I(t) gives:

${I(t)} = {{{\frac{- 1}{RC}\left\lbrack {{V_{c\; 0}C} + \frac{\omega \; V_{m}}{R\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack}} \right\rbrack}e^{\frac{- t}{RC}}} + {{\frac{V_{m}}{R}\left\lbrack \frac{1}{\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack} \right\rbrack}\left\lbrack {{\omega^{2}{\sin \left( {\omega \; t} \right)}} + {\frac{\omega}{RC}\cos \; \omega \; t}} \right\rbrack}}$

where V_(c0) is the initial value of the capacitor voltage, V_(m) is themagnitude of the driving sine wave, and ω is the radian frequency (2πf).

The first term contains the terms defining the non-steady statecondition. One way to speed the settling of the system would be to havethe first term equal 0, which may be done, e.g., by setting

${V_{cinit}C} = \frac{\omega \; V_{m}}{R\left\lbrack {\omega^{2} + \frac{1}{R^{2}C^{2}}} \right\rbrack}$or$V_{cinit} = \frac{{RC}\; \omega \; V_{m}}{\left\lbrack {{R^{2}C^{2}\omega^{2}} + 1} \right\rbrack}$

While this may not be necessary in practice, it is possible to set theinitial phase of the forcing sine wave to jump immediately from the DCsteady state point to V_(cinit). This technique may be evaluated for thespecific frequency and anticipated phase angle to find the possiblereduction in time.

The non-steady state term is multiplied by the exponential function oftime. This will determine how quickly the steady state condition isreached. The RC value can be determined as a first order approximationfrom the impedance calculation information. Given the following:

$X_{c} = {\frac{1}{\omega \; C} = {Z\mspace{20mu} \sin \; \varphi}}$and R = Z  cos  φ,

it follows that

${RC} = {\frac{Z\mspace{14mu} \cos \; \varphi}{\omega \; Z\mspace{14mu} \sin \; \varphi} = \frac{1}{\omega \mspace{14mu} \tan \; \varphi}}$

For a sensor at 100 Hz with a 5 degree phase angle, this would mean atime constant of 18.2 msec. For settling to less than 1%, this wouldmean approximately 85 msec settling time or 8.5 cycles. On the otherhand, for a sensor at 0.10 Hz with a 65 degree phase angle, this wouldmean a time constant of 0.75 sec. For settling to less than 1%, thiswould mean approximately 3.4 sec settling time.

Thus, in embodiments of the invention as detailed hereinabove, the ASICincludes (at least) 7 electrode pads, 5 of which are assigned as WORKelectrodes (i.e., sensing electrodes, or working electrodes, or WEs),one of which is labeled COUNTER (i.e., counter electrode, or CE), andone that is labeled REFERENCE (i.e., reference electrode, or RE). Thecounter amplifier 4321 (see FIG. 42B) may be programmably connected tothe COUNTER, the REFERENCE, and/or any of the WORK assigned pads, and inany combination thereof. As has been mentioned, embodiments of theinvention may include, e.g., more than five WEs. In this regard,embodiments of the invention may also be directed to an ASIC thatinterfaces with more than 5 working electrodes.

It is important to note that, with the ASIC as described herein, each ofthe above-mentioned five working electrodes, the counter electrode, andthe reference electrode is individually and independently addressable.As such, any one of the 5 working electrodes may be turned on andmeasure Isig (electrode current), and any one may be turned off.Moreover, any one of the 5 working electrodes may be operablyconnected/coupled to the EIS circuitry for measurement of EIS-relatedparameters, e.g., impedance and phase. In other words, EIS may beselectively run on any one or more of the working electrodes. Inaddition, the respective voltage level of each of the 5 workingelectrodes may be independently programmed in amplitude and sign withrespect to the reference electrode. This has many applications, such as,e.g., changing the voltage on one or more electrodes in order to makethe electrode(s) less sensitive to interference.

In embodiments where two or more working electrodes are employed asredundant electrodes, the EIS techniques described herein may be used,e.g., to determine which of the multiplicity of redundant electrodes isfunctioning optimally (e.g., in terms of faster start-up, minimal or nodips, minimal or no sensitivity loss, etc.), so that only the optimalworking electrode(s) can be addressed for obtaining glucosemeasurements. The latter, in turn, may drastically reduce, if noteliminate, the need for continual calibrations. At the same time, theother (redundant) working electrode(s) may be: (i) turned off, whichwould facilitate power management, as EIS may not be run for the “off”electrodes; (ii) powered down; and/or (iii) periodically monitored viaEIS to determine whether they have recovered, such that they may bebrought back on line. On the other hand, the non-optimal electrode(s)may trigger a request for calibration. The ASIC is also capable ofmaking any of the electrodes—including, e.g., a failed or off-lineworking electrode—the counter electrode. Thus, in embodiments of theinvention, the ASIC may have more than one counter electrode.

While the above generally addresses simple redundancy, wherein theredundant electrodes are of the same size, have the same chemistry, thesame design, etc., the above-described diagnostic algorithms, fusionmethodologies, and the associated ASIC may also be used in conjunctionwith spatially distributed, similarly sized or dissimilarly sized,working electrodes as a way of assessing sensor implant integrity as afunction of implant time. Thus, in embodiments of the invention, sensorsmay be used that contain electrodes on the same flex that may havedifferent shapes, sizes, and/or configurations, or contain the same ordifferent chemistries, used to target specific environments.

For example, in one embodiment, one or two working electrodes may bedesigned to have, e.g., considerably better hydration, but may not lastpast 2 or 3 days. Other working electrode(s), on the other hand, mayhave long-lasting durability, but slow initial hydration. In such acase, an algorithm may be designed whereby the first group of workingelectrode(s) is used to generate glucose data during early wear, afterwhich, during mid-wear, a switch-over may be made (e.g., via the ASIC)to the second group of electrode(s). In such a case, the fusionalgorithm, e.g., may not necessarily “fuse” data for all of the WEs, andthe user/patient is unaware that the sensing component was switchedduring mid-wear.

In yet other embodiments, the overall sensor design may include WEs ofdifferent sizes. Such smaller WEs generally output a lower Isig (smallergeometric area) and may be used specifically for hypoglycemiadetection/accuracy, while larger WEs—which output a larger Isig—may beused specifically for euglycemia and hyperglycemia accuracy. Given thesize differences, different EIS thresholds and/or frequencies must beused for diagnostics as among these electrodes. The ASIC, as describedhereinabove, accommodates such requirements by enabling programmable,electrode-specific, EIS criteria. As with the previous example, signalsmay not necessarily be fused to generate an SG output (i.e., differentWEs may be tapped at different times).

As was noted previously, the ASIC includes a programmable sequencer 4266that commands the start and stop of the stimulus and coordinates themeasurements of the EIS-based parameters for frequencies above about 100Hz. At the end of the sequence, the data is in a buffer memory, and isavailable for a microprocessor to quickly obtain (values of) the neededparameters. This saves time, and also reduces system power requirementsby requiring less microprocessor intervention.

For frequencies lower than about 100 Hz, the programmable sequencer 4266coordinates the starting and stopping of the stimulus for EIS, andbuffers data. Either upon the end of the measurement cycle, or if thebuffer becomes close to full, the ASIC may interrupt the microprocessorto indicate that it needs to gather the available data. The depth of thebuffer will determine how long the microprocessor can do other tasks, orsleep, as the EIS-based parameters are being gathered. For example, inone preferred embodiment, the buffer is 64 measurements deep. Again,this saves energy as the microprocessor will not need to gather the datapiecemeal. It is also noted that the sequencer 4266 also has thecapability of starting the stimulus at a phase different from 0, whichhas the potential of settling faster.

The ASIC, as described above, can control the power to a microprocessor.Thus, for example, it can turn off the power completely, and power upthe microprocessor, based on detection of sensorconnection/disconnection using, e.g., a mechanical switch, or capacitiveor resistive sensing. Moreover, the ASIC can control the wakeup of amicroprocessor. For example, the microprocessor can put itself into alow-power mode. The ASIC can then send a signal to the microprocessorif, e.g., a sensor connect/disconnect detection is made by the ASIC,which signal wakes up the processor. This includes responding to signalsgenerated by the ASIC using techniques such as, e.g., a mechanicalswitch or a capacitive-based sensing scheme. This allows themicroprocessor to sleep for long periods of time, thereby significantlyreducing power drain.

It is important to reiterate that, with the ASIC as describedhereinabove, both oxygen sensing and peroxide sensing can be performedsimultaneously, because the five (or more) working electrodes are allindependent, and independently addressable, and, as such, can beconfigured in any way desired. In addition, the ASIC allows multiplethresholds for multiple markers, such that EIS can be triggered byvarious factors—e.g., level of V_(cntr), capacitance change, signalnoise, large change in Isig, drift detection, etc.—each having its ownthreshold(s). In addition, for each such factor, the ASIC enablesmultiple levels of thresholds.

In yet another embodiment of the invention, EIS may be used as analternative plating measurement tool, wherein the impedance of both theworking and counter electrodes of the sensor substrate may be tested,post-electroplating, with respect to the reference electrode. Morespecifically, existing systems for performing measurements of the sensorsubstrate which provide an average roughness of the electrode surfacesample a small area from each electrode to determine the averageroughness (Ra) of that small area. For example, currently, the ZygoNon-contact Interferometer is used to quantify and evaluate electrodesurface area. The Zygo interferometer measures a small area of thecounter and working electrodes and provides an average roughness value.This measurement correlates the roughness of each sensor electrode totheir actual electrochemical surface area. Due to the limitations ofsystems that are currently used, it is not possible, from amanufacturing throughput point of view, to measure the entire electrodesurface, as this would be an extremely time-consuming endeavor.

In order to measure the entire electrode in a meaningful andquantitative manner, an EIS-based methodology for measuring surface areahas been developed herein that is faster than current, e.g., Zygo-based,testing, and more meaningful from a sensor performance perspective.Specifically, the use of EIS in electrode surface characterization isadvantageous in several respects. First, by allowing multiple plates tobe tested simultaneously, EIS provides a faster method to testelectrodes, thereby providing for higher efficiency and throughput,while being cost-effective and maintaining quality.

Second, EIS is a direct electrochemical measurement on the electrodeunder test, i.e., it allows measurement of EIS-based parameter(s) forthe electrode and correlates the measured value to the trueelectrochemical surface area of the electrode. Thus, instead of takingan average height difference over a small section of the electrode, theEIS technique measures the double layer capacitance (which is directlyrelated to surface area) over the whole electrode surface area and, assuch, is more representative of the properties of the electrode,including the actual surface area. Third, EIS testing is non-destructiveand, as such, does not affect future sensor performance. Fourth, EIS isparticularly useful where the surface area to be measured is eitherfragile or difficult to easily manipulate.

For purposes of this embodiment of the invention, the EIS-basedparameter of interest is the Imaginary impedance (Zim), which may beobtained, as discussed previously, based on measurements of theimpedance magnitude (|Z|) in ohms and the phase angle (Φ) in degrees ofthe electrode immersed in an electrolyte. It has been found that, inaddition to being a high-speed process, testing using theelectrochemical impedance of both the Counter Electrode (CE) and the WEis an accurate method of measuring the surface area of each electrode.This is also important because, although the role of electrode size inglucose sensor performance is dictated, at least in part, by theoxidation of the hydrogen peroxide produced by the enzymatic reaction ofglucose with GOX, experiments have shown that an increased WE surfacearea reduces the number of low start-up events and improves sensorresponsiveness—both of which are among the potential failure modes thatwere previously discussed at some length.

Returning to the imaginary impedance as the EIS-based parameter ofinterest, it has been found that the key parameters that drive theelectrode surface area, and consequently, its imaginary impedance valuesare: (i) Electroplating conditions (time in seconds and current in microAmperes); (ii) EIS frequency that best correlates to surface area; (iii)the number of measurements conducted on a single electrode associated tothe electrolyte used in the EIS system; and (iv) DC Voltage Bias.

In connection with the above parameters, experiments have shown thatusing Platinum plating solution as the electrolyte presents a poorcorrelation between the imaginary impedance and surface area across theentire spectrum. However, using Sulfuric Acid (H2SO4) as the electrolytepresents very good correlation data, and using Phosphate Buffered salineSolution with zero mg/ml of Glucose (PBS-0) presents even bettercorrelation data, between imaginary impedance and Surface Area Ratio(SAR), especially between the relatively-lower frequencies of 100 Hz and5 Hz. Moreover, fitted regression analysis using a cubic regressionmodel indicates that, in embodiments of the invention, the bestcorrelation may occur at a frequency of 10 Hz. In addition, it has beenfound that reducing the Bias voltage from 535 mV to zero dramaticallyreduces the day-to-day variability in the imaginary impedancemeasurement.

Using the above parameters, the limits of acceptability of values ofimaginary impedance can be defined for a given sensor design. Thus, forexample, for the Comfort Sensor manufactured by Medtronic Minimed, theimaginary impedance measured between the WE and the RE (Platinum mesh)must be greater than, or equal to, −100 Ohms. In other words, sensorswith an imaginary impedance value (for the WE) of less than −100 Ohmswill be rejected. For the WE, an impedance value of greater than, orequal to, −100 Ohms corresponds to a surface area that is equal to, orgreater than, that specified by an equivalent Ra measurement of greaterthan 0.55 um.

Similarly, the imaginary impedance measured between the CE and the RE(Platinum mesh) must be greater than, or equal to, −60 Ohms, such thatsensors with an imaginary impedance value (for the CE) of less than −60Ohms will be rejected. For the CE, an impedance value of greater than,or equal to, −60 Ohms corresponds to a surface area that is equal to, orgreater than, that specified by an equivalent Ra measurement greaterthan 0.50 um.

In accordance with embodiments of the invention, an equivalent circuitmodel as shown in FIG. 48 may be used to model the measured EIS betweenthe working and reference electrodes, WE and RE, respectively. Thecircuit shown in FIG. 48 has a total of six (6) elements, which may bedivided into three general categories: (i) reaction-related elements;(ii) Membrane-related elements; and (iii) solution-related elements. Inthe latter category, Rsol is the solution resistance, and corresponds tothe properties of the environment external to the sensor system (e.g.,interstitial fluid in vivo).

The reaction-related elements include R_(p), which is the polarizationresistance (i.e., resistance to voltage bias and charge transfer betweenthe electrode and electrolyte), and Cdl, which is the double layercapacitance at the electrode-electrolyte interface. It is noted that,while, in this model, the double layer capacitance is shown as aconstant phase element (CPE) due to inhomogeneity of the interface, itcan also be modeled as a pure capacitance. As a CPE, the double layercapacitance has two parameters: Cdl, which denotes the admittance, andα, which denotes the constant phase of the CPE (i.e., how leaky thecapacitor is). The frequency-dependent impedance of the CPE may becalculated as

$Z_{CPE} = {\frac{1}{{{Cdl}\left( {j\; \omega} \right)}^{\alpha}}.}$

Thus, the model includes two (2) reaction-related elements—R_(p) andCdl—which are represented by a total of three (3) parameters: R_(p),Cdl, and α.

The membrane-related elements include Rmem, which is the membraneresistance (or resistance due to the chemistry layer), and Cmem, whichis the membrane capacitance (or capacitance due to the chemistry layer).Although Cmem is shown in FIG. 48 as a pure capacitance, it can also bemodeled as a CPE in special cases. As shown, W is the bounded Warburgelement, and has two parameters: Y₀, which denotes the admittance of theWarburg element due to glucose/H₂O₂ diffusion within the chemistrylayer, and λ, which denotes the diffusion time constant of the Warburgelement. It is noted that Warburg may also be modeled in other ways(e.g., unbounded). The frequency-dependent impedance of the boundedWarburg element may be calculated as

$Z_{W} = {\frac{1}{Y_{0}\sqrt{j\; \omega}} \times {\coth \left( {\lambda \sqrt{j\; \omega}} \right)}}$

Thus, the model includes three (3) membrane-related elements—Rmem, Cmem,and W—which are represented by a total of four (4) parameters: Rmem,Cmem, Y₀, and λ.

The top portion of FIG. 48 shows the overall structure of a sensor inaccordance with embodiments of the invention, where Platinum Blackrefers to the electrode. Here, it is important to note that, while asingle electrode is depicted, this is by way of illustration only, andnot limitation, as the model may be applied to sensors having a greaternumber of layers, and a larger number of electrodes, than theillustrative 3-layer, single-electrode structure shown in FIG. 48. Asdescribed previously herein, GLM is the sensor's glucose limitingmembrane, HSA is human serum albumin, GOX is glucose oxidase enzyme(used as the catalyst), and Solution refers to the environment in whichthe electrode is disposed, such as, e.g., a user's bodily fluid(s).

In the ensuing discussion, the equivalent circuit model of FIG. 48 willbe used to explain some of the physical properties of the sensorbehavior. Nevertheless, it should be mentioned that, depending on howthe glucose diffusion is modeled, other circuit configurations may alsobe possible. In this regard, FIGS. 49A-49C show illustrations of someadditional circuit models, some of which include a larger number ofelements and/or parameters. For purposes of the invention, however, ithas been discovered that the circuit model of FIG. 48, wherein the masstransport limitation—i.e., the Warburg component—is attributed toglucose diffusion through the membrane, provides the best fit vis-à-visempirical data. FIG. 50A is a Nyquist plot showing that the equivalentcircuit simulation 5020 fits the empirical data 5010 very closely. FIG.50B is an enlarged diagram of the high-frequency portion of FIG. 50A,showing that the simulation tracks the actual sensor data quiteaccurately in that region as well.

Each of the above-described circuit elements and parameters affects theEIS output in various ways. FIG. 51 shows a Nyquist plot, wherein Cdlincreases in the direction of Arrow A. As can be seen, as the value ofCdl increases, the length of the (lower frequency) Nyquist plotdecreases, and its slope increases. Thus, the length of the Nyquist plotdecreases from plot 5031 to plot 5039, with each of plots 5033, 5035,and 5037 having respective lengths that progressively decrease as Cdlincreases from plot 5031 to plot 5039. Conversely, the slope of theNyquist plot increases from plot 5031 to plot 5039, with each of plots5033, 5035, and 5037 having respective slopes that progressivelyincrease as Cdl increases from plot 5031 to plot 5039. Thehigher-frequency region of the Nyquist plot, however, is generally notaffected.

FIG. 52 shows a Nyquist plot, wherein a increases in the direction ofArrow A. Here, as a increases, the slope of the Nyquist plot increasesin the lower frequency region. In FIG. 53, as R_(p) increases in thedirection of Arrow A, the length and the slope of the lower-frequencyNyquist plot increase. The higher the Rp, the higher the amount ofresistance to the chemical reaction and, therefore, the slower the rateof electron and ion exchange. Thus, phenomenologically, FIG. 53 showsthat the length and the slope of the lower-frequency Nyquist plotincrease as the electron-ion exchange rate decreases—i.e., as theresistance to the chemical reaction increases, which, in turn, means alower current (Isig) output. Again, there is minimal to no effect on thehigher-frequency region of the Nyquist plot.

The effect of change in the Warburg admittance is shown in FIG. 54. Asthe Warburg admittance increases in the direction of Arrow A, both thelength and the slope of the lower-frequency Nyquist plot increase.Phenomenologically, this means that the length and the slope of thelower-frequency Nyquist plot tend to increase as the influx of thereactant increases. In FIG. 55, as λ increases in the direction of ArrowA, the slope of the Nyquist plot decreases.

In contrast to the above-described elements and parameters, themembrane-related elements and parameters generally affect thehigher-frequency region of the Nyquist plot. FIG. 56 shows the effect ofthe membrane capacitance on the Nyquist plot. As can be seen from FIG.56, changes in Cmem affect how much of the high-frequency region'ssemi-circle is visible. Thus, as membrane capacitance increases in thedirection of Arrow A, progressively less of the semi-circle can be seen.Similarly, as shown in FIG. 57, as the membrane resistance increases inthe direction of Arrow A, more of the high-frequency region semi-circlebecomes visible. In addition, as Rmem increases, the overall Nyquistplot shifts from left to right. The latter parallel-shifting phenomenonalso holds true for Rsol, as shown in FIG. 58.

The above discussion in connection with the equivalent circuit model ofFIG. 48 may be summarized as follows. First, Cdl, α, Rp, Warburg, and λgenerally control the low frequency response. More specifically, thelower-frequency Nyquist slope/Zimag primarily depends on Cdl, α, Rp, andλ, and the lower-frequency length/Zmagnitude primarily depends on Cdl,Rp, and Warburg Admittance. Second, Rmem and Cmem control thehigher-frequency response. In particular, Rmem determines the highfrequency semi-circle diameter, and Cmem determines the turning pointfrequency, having minimal overall effect on the Nyquist plot. Lastly,changes in Rmem and Rsol cause parallel shifts in the Nyquist plot.

FIGS. 59A-59C, 60A-60C, and 61A-61C show results of in-vitro experimentsfor changes in the above-described circuit elements during sensorstart-up and calibration. FIGS. 59A, 60A, and 61A are identical. Asshown in FIG. 59A, the experiments were generally run with two redundantworking electrodes 5050, 5060, and for a period of (between 7 and) 9days. A baseline glucose amount of 100 mg/dL was used, although thelatter was changed between zero and 400 mg/dL at various pointsthroughout the experiment (5070). In addition, the effects of a(solution) temperature change between 32° C. and 42° C. (5080) and a 0.1mg/dL acetaminophen response (5085) were explored. Lastly, theexperiments included an Oxygen stress test, where the supply of Oxygendissolved in the solution was varied (i.e., limited) between 0.1% and 5%(5075). For purposes of these experiments, a full EIS sweep (i.e., from0.1 Hz-8 kHz) was run, and the output data was recorded (and plotted)about once every 30 minutes. However, shorter or longer intervals mayalso be used.

In FIG. 59C, the sum of Rsol and Rmem—which, again, may be estimated bythe magnitude of real impedance at the inflection point of the Nyquistplot—displays a general downwards trend as a function of time. This isdue primarily to the fact that the membrane takes time to hydrate, suchthat, as time passes by, it will become less resistant to the electricalcharges. A slight correlation can also be seen between the plot for Isig(FIG. 59A) and that for Rsol+Rmem (FIG. 59C).

FIG. 60B shows the EIS output for Cdl. Here, there is initially arelatively rapid drop (5087), over a period of several hours, due to thesensor activation/sensor charge-up process. Thereafter, however, Cdlremains fairly constant, exhibiting a strong correlation with Isig (FIG.60A). Given the latter correlation, Cdl data, as an EIS parameter, maybe less useful in applications where glucose independence is desired. Asshown in FIG. 60C, the trend for Rp may be generally described as amirror image of the plot for Cdl. As the membrane becomes more hydrated,the influx increases, which is reflected in the plot of Warburgadmittance in FIG. 61B. As shown in FIG. 61C, λ remains generallyconstant throughout.

FIGS. 62-65 show the actual EIS response for various parts of theabove-described experiments. Specifically, the changes that were madeduring the first 3 days—i.e., glucose changes, Oxygen stress, andtemperature changes, as shown in FIGS. 59A, 60A, and 61A—are boxed(5091) in FIG. 62, with the Vcntr response 5093 being shown in thebottom portion of this Figure and in FIG. 59B. FIG. 63 shows that anIsig calibration via an increase in glucose caused the slope and lengthof the Nyquist plot to decrease. In FIG. 64, the Oxygen (or Vcntr)response is shown in Day 2, where Vcntr becomes more negative as theOxygen content is decreased. Here, the Nyquist plot becomes shorter inlength, and its slope decreases (5094), indicating a large decrease inimaginary impedance. The plot length depends primarily on Cdl and Rp,and is strongly correlated to Vcntr which, in turn, responds to changesin glucose and Oxygen. In FIG. 65, the Isig changes negligibly from Day2 to Day 3. Nevertheless, the Nyquist plot shifts horizontally (from theplot at 37° C.) for data taken at 32° C. (5095) and at 42° C. (5097).However, there is no significant impact on Nyquist plot length, slope,or Isig.

Putting the above-described EIS output and signature informationtogether, it has been discovered that, during sensor start-up, themagnitude of Rmem+Rsol decreases over time, corresponding to a shiftfrom right to left in the Nyquist plot. During this period, Cdldecreases, and Rp increases, with a corresponding increase in Nyquistslope. Finally, Warburg admittance also increases. As noted previously,the foregoing is consistent with the hydration process, with EIS plotsand parameter values taking on the order of 1-2 days (e.g., 24-36 hours)to stabilize.

Embodiments of the invention are directed to real-time self-calibration,and more particularly, to in-vivo self-calibration of glucose sensorsbased on EIS data. Any calibration algorithm, including self-calibrationalgorithms, must address sensitivity loss. As discussed previously, twotypes of sensitivity loss may occur: (1) Isig dip, which is a temporaryloss of sensitivity, typically occurring during the first few days ofsensor operation; and (2) permanent sensitivity loss, occurringgenerally at the end of sensor life, and sometimes correlated with thepresence of a Vcntr rail.

It has been discovered that sensitivity loss can manifest itself as anincrease in Rsol or Rmem (or both), which can be observed in the Nyquistplot as a parallel shift to the right, or, if Rmem changes, a morevisible start to a semicircle at the higher frequencies (resulting in anincrease in high-frequency imaginary impedance). In addition to, orinstead of, Rsol and Rmem, there could be an increase in Cmem only. Thiscan be observed as changes in the high-frequency semicircle. Sensitivityloss will be accompanied by a change in Cdl (by way of a longer tail inthe lower-frequency segment of the Nyquist plot). The foregoingsignatures provide a means for determining how different changes in EISoutput can be used to compensate for changes in sensitivity.

For a normally operating glucose sensor, there is a linear relationshipbetween blood glucose (BG) and the sensor's current output (Isig). Thus,

BG=CF×(Isig+c)

where “CF” is the Cal Factor, and “c” is the offset. This is shown inFIG. 66, where the calibration curve is as shown by line 6005, and “c”is the baseline offset 6007 (in nA). However, when there is an increasein Rmem and/or a decrease in Cmem, then c will be affected. Thus, line6009 depicts a situation in which Rmem increases and Cmemdecreases—which signifies changes in the membrane properties—therebycausing the offset “c” to move to 6011, i.e., a downward shift of thecalibration curve. Similarly, when there are (non-glucose related)changes in Cdl and increases in Rp—with a resultant increase in thelength of the (lower-frequency) Nyquist plot—then the slope will beaffected, where the slope=1/CF. Thus, in FIG. 66, line 6013 has adifferent (smaller) slope that line 6005. Combined changes can alsooccur, which is illustrated by line 6015, indicating sensitivity loss.

The length of the lower-frequency segment of the Nyquist plot(L_(nyquist))—which, for simplicity, may be illustratively estimated asthe length between 128 Hz and 0.105 Hz (real) impedance—is highlycorrelated with glucose changes. It has been discovered, through modelfitting, that the only parameter that changes during glucose changes isthe double layer capacitance Cdl, and specifically the double layeradmittance. Therefore the only Isig-dependent—and, by extension,glucose-dependent—parameter in the equivalent circuit model of FIG. 48is Cdl, with all other parameters being substantially Isig-independent.

In view of the above, in one embodiment of the invention, changes inRmem and Cmem may be tracked to arrive at a readjustment of the CalFactor (BG/Isig) and, thereby, enable real-time self-calibration ofsensors without the need for continual finger-stick testing. This ispossible, in part, because changes in Rmem and Cmem result in a changein the offset (c), but not in the slope, of the calibration curve. Inother words, such changes in the membrane-related parameters of themodel generally indicate that the sensor is still capable of functioningproperly.

Graphically, FIG. 67A shows actual blood glucose (BG) data 6055 that isbeing recorded, overlaid by the Isig output 6060 from the workingelectrode. Comparing the data from a first period (or time window)comprising approximately days 1-4 (6051) with the data from a secondperiod comprising approximately days 6-9 (6053), FIG. 67A shows that thesensor is drifting generally downwards during the second time period,indicating perhaps a moderate sensitivity loss in the sensor. There isalso an increase in Vcntr during the second time period, as shown inFIG. 67B.

With reference to FIGS. 68 and 69, it can be seen that the sensitivityloss is clearly shown by a rather significant increase in membraneresistance 6061, as well as a corresponding drop in Warburg Admittance6063, during the second time period between days 6 and 9. Accordingly,FIG. 70 shows that the calibration curve 6073 for the second time period6053 is parallel to, but shifted down from, the calibration curve 6071for the first time period 6051. Also, as discussed hereinabove inconnection with FIG. 57, as the membrane resistance (Rmem) increases,overall Nyquist plot shifts from left to right, and more of thehigh-frequency region semi-circle becomes visible. For the data of FIGS.67A-70, this phenomenon is shown in FIG. 71, where the enlargedhigher-frequency region of the Nyquist plot shows that the data from thesecond time period 6053 moves the plot from left to right as comparedwith the data from the first time period 6051, and that the semi-circlebecomes more and more visible (6080) as the shift in the Nyquist plotprogresses from left to right. In addition, the enlarged lower-frequencyregion of the plot shows that there is no significant change inL_(nyquist).

Changes in Cdl and Rp, on the other hand, generally indicate that theelectrode(s) may already be compromised, such that recovery may nolonger be possible. Still, changes in Cdl and Rp may also be tracked,e.g., as a diagnostic tool, to determine, based on the direction/trendof the change in these parameters, whether, the drift or sensitivityloss has in fact reached a point where proper sensor operation is nolonger recoverable or achievable. In this regard, in embodiments of theinvention, respective lower and/or upper thresholds, or ranges ofthresholds, may be calculated for each of Cdl and Rp, or for the changein slope, such that EIS output values for these parameters that falloutside of the respective threshold (range) may trigger, e.g.,termination and/or replacement of the sensor due to unrecoverablesensitivity loss. In specific embodiments, sensor-design and/orpatient-specific ranges or thresholds may be calculated, wherein theranges/thresholds may be, e.g., relative to the change in Cdl, Rp,and/or slope.

Graphically, FIG. 72A shows actual blood glucose (BG) data 6155 that isbeing recorded, overlaid by the Isig output from two working electrodes,WE1 6160 and WE2 6162. The graphs show data from a first time window forday 1 (6170), a second time window for days 3-5 (6172), a third timewindow for day 3 (6174), and a fourth time window for days 5½ to 9½(6176). Starting on Day 3, FIG. 72B shows that Vcntr rails at 1.2 volts.However, the decrease in sensitivity occurs from about Day 5 or so(6180). Once the Vcntr rails, the Cdl increases significantly, with acorresponding decrease in Rp, signifying a higher resistance to theoverall electrochemical reaction. As expected, the slope of thecalibration curve also changes (decreases), and L_(nyquist) becomesshorter (see FIGS. 73-75). It is noted that, in embodiments of theinvention, the occurrence of a Vcntr rail may be used to triggertermination of a sensor as unrecoverable.

The combined effect of the increase in membrane resistance, the decreasein Cdl, and Vcntr rail is shown in FIGS. 76A-76B and 77-80. In FIG. 76A,actual blood glucose (BG) data 6210 is overlaid by the Isig output fromtwo working electrodes, WE1 6203 and WE2 6205. As can be seen, WE1generally tracks the actual BG data 6210—i.e., WE1 is functioningnormally. The Isig from WE2, on the other hand, appears to start at alower point, and continues a downwards trend all the way from thebeginning to Day 10, thus signifying a gradual loss of sensitivity. Thisis consistent with the Cdl for WE2 (6215) being lower than that for WE1(6213), as shown in FIG. 77, even though the Cdl for both workingelectrodes generally exhibits a downward trend.

FIG. 79 shows the combined effect on the calibration curve, where boththe offset and the slope of the linear fit for the period of sensitivityloss (6235) change relative to the calibration curve 6231 for thenormally-functioning time windows. In addition, the Nyquist plot of FIG.80 shows that, in the lower-frequency region, the length of the Nyquistplot is longer where there is sensitivity loss (6245), as compared towhere the sensor is functioning normally (6241). Moreover, near theinflection point, the semicircles (6255) become more and more visiblewhere there is loss of sensitivity. Importantly, where there issensitivity loss, the Nyquist plot of FIG. 80 shifts horizontally fromleft to right as a function of time. In embodiments of the invention,the latter shift may be used as a measure for compensation orself-correction in the sensor.

Thus, it has been discovered that, as an EIS signature, a temporary dipmay be caused by increased membrane resistance (Rmem) and/or local Rsolincrease. An increase in Rmem, in turn, is reflected by increasedhigher-frequency imaginary impedance. This increase may be characterizedby the slope at high frequencies, (S_(nyquist))—which, for simplicity,may be illustratively estimated as the slope between 8 kHz and 128 Hz.In addition, Vcntr railing increases Cdl and decrease Rp, such that thelength and slope decrease; this may be followed by gradual Cdl decreaseand Rp increase associated with sensitivity loss. In general, a decreasein Cdl, combined with an increase in Rp (length increase) and in Rmemmay be sufficient to cause sensitivity loss.

In accordance with embodiments of the invention, an algorithm for sensorself-calibration based on the detection of sensitivity change and/orloss is shown in FIG. 81. At blocks 6305 and 6315, a baseline Nyquistplot length (L_(nyquist)) and a baseline higher frequency slope,respectively, are set, so as to be reflective of the EIS state at thebeginning of sensor life. As noted, the Nyquist plot length iscorrelated to the Cdl, and the higher frequency Nyquist slope iscorrelated to the membrane resistance. The process then continues bymonitoring the Nyquist plot length (6335) and the higher frequency slope(6345), as well as the Vcntr value (6325). When the Vcntr rails, thebaseline L_(nyquist) is adjusted, or reset 6355, as the railing of theVcntr changes the Cdl significantly. There is therefore a feedback loop6358 to accommodate real-time changes in the monitored EIS parameters.

As shown in block 6375, as the length of the Nyquist plot is monitored,a significant increase in that length would indicate reducedsensitivity. In specific embodiments, sensor-design and/orpatient-specific ranges or thresholds may be calculated, wherein theranges/thresholds may be, e.g., relative to the change in the length ofthe Nyquist plot. Similarly, a more negative higher-frequency slopeS_(nyquist) corresponds to an increased appearance of the high-frequencysemicircle and would be indicative of a possible dip 6365. Any suchchanges in L_(nyquist) and S_(nyquist) are monitored, e.g., eithercontinuously or periodically and, based on the duration and trend of thereduction in sensitivity, a determination is made as to whether total(i.e., severe) sensitivity loss has occurred, such that specific sensorglucose (SG) value(s) should be discarded (6385). In block 6395, the CalFactor may be adjusted based on the monitored parameters, so as toprovide a “calibration-free” CGM sensor. It is noted that, within thecontext of the invention, the term “calibration-free” does not mean thata particular sensor needs no calibration at all. Rather, it means thatthe sensor can self-calibrate based on the EIS output data, in realtime, and without the need for additional finger-stick or meter data. Inthis sense, the self-calibration may also be referred to as“intelligent” calibration, as the calibration is not performed based ona predetermined temporal schedule, but on an as-needed basis, inreal-time.

In embodiments of the invention, algorithms for adjustment of the CalFactor (CF) and/or offset may be based on the membrane resistance which,in turn, may be estimated by the sum of Rmem and Rsol. As membraneresistance is representative of a physical property of the sensor, itgenerally cannot be estimated from EIS data run for a single frequency.Put another way, it has been observed that no single frequency willconsistently represent membrane resistance, since frequencies shiftdepending on sensor state. Thus, FIG. 82, e.g., shows that, when thereis some sensitivity loss, there is a horizontal shift in the Nyquistplot, and therefore, a shift in the inflection point that estimates thevalue of Rmem+Rsol. In this case, the shift in the real component ofimpedance is actually quite large. However, if only the high-frequency(e.g., at 8 kHz) real impedance is monitored, there is little to noshift at all, as indicated by the encircled region in FIG. 82.

There is therefore a need to track membrane resistance in a physicallymeaningful way. Ideally, this may be done through model fitting, whereRmem and Rsol are derived from model fitting, and Rm is calculated asRm=Rmem+Rsol. However, in practice, this approach is not onlycomputationally expensive, as it may take an unpredictably long amountof time, but also susceptible to not converging at all in somesituations. Heuristic metrics may therefore be developed to approximate,or estimate, the value of Rm=Rmem+Rsol. In one such metric, Rmem+Rsol isapproximated by the value of the real-impedance intercept at a fairlystable imaginary impedance value. Thus, as shown in FIG. 83, forexample, a region of general stability for the imaginary impedance (onthe Y axis) may be identified at about 2000Ω. Taking this as a referencevalue and traveling across, parallel to the X axis, a value proportionalto Rm may then be approximated as the real-impedance value of where thereference line crosses the Nyquist plot. An interpolation betweenfrequencies may be performed to estimate ΔRm ∝Δ (Rmem+Rsol).

Having estimated the value of Rm as discussed above, the relationshipbetween Rm and the Cal Factor (CF) and/or Isig may then be explored.Specifically, FIG. 84 shows the relationship between the estimated Rmand CF, wherein the former is directly proportional to the latter. Thedata points for purposes of FIG. 84 were derived for steady state sensoroperation. FIG. 85 shows a plot of normalized Isig vs. 1/Rm, where Isighas been normalized by the BG range (of the Isig). As can be seen fromthe figure, Isig can be adjusted based on changes in Rm. Specifically,an increase in 1/Rm (i.e., reduced membrane resistance) will lead to aproportional increase in Isig, as there is a linear relationship betweenIsig and 1/Rm.

Thus, in one embodiment, an algorithm for adjustment of the Cal Factorwould entail monitoring the change in membrane resistance based on areference Cal Factor, and then modifying the Cal Factor proportionallybased on the correlation between Rm and CF. In other words:

$\left. {\frac{d({CF})}{d\; t} \propto \frac{d({Rm})}{d\; t}}\Rightarrow{{{Adjusted}\mspace{14mu} {CF}} \propto {\left( \frac{d({Rm})}{d\; t} \right) \times {CF}}} \right.$

In another embodiment, a Cal Factor adjustment algorithm may entailmodification of Isig based on proportional changes in 1/Rm, andindependently of CF calculations. Thus, for purposes of such analgorithm, the adjusted Isig is derived as

${{Adjusted}\mspace{14mu} {Isig}} \propto {\left( \frac{d\left( \frac{1}{R_{m}} \right)}{d\; t} \right) \times {Isig}}$

Experiments have shown that the most dramatic CF changes occur in first8 hours of sensor life. Specifically, in one set of in-vitroexperiments, Isig was plotted as a function of time, while keepingvarious glucose levels constant over the life of the sensor. EIS was runevery 3 minutes for the first 2 hours, while all model parameters wereestimated and tracked over time. As noted previously, given a limitedspectrum EIS, Rmem and Rsol cannot be (independently) estimatedrobustly. However, Rm=Rmem+Rsol can be estimated.

FIG. 86 shows the plots for Isig over time for various glucose levels,including 400 mg/dL (6410), 200 mg/dL (6420), 100 mg/dL (6430), 60 mg/dL(6440), and 0 mg/dL (6450). At startup, generally dramatic changesappear in all parameters. One example is shown in FIG. 87, where Cdl isplotted as a function of time, with plot 6415 corresponding to 400 mg/dLglucose, plot 6425 corresponding to 200 mg/dL glucose, plot 6435corresponding to 100 mg/dL glucose, plot 6445 corresponding to 60 mg/dLglucose, and plot 6455 corresponding to 0 mg/dL glucose. As is the casein the illustrative example of FIG. 87, most parameters correlate wellwith changes in the first 0.5 hour, but generally may not account forchanges in timeframes>0.5 hour.

It has been discovered, however, that Rm=Rmem+Rsol is the only parameterthat can account for changes in Isig over a similar startup time frame.Specifically, FIG. 88 shows the same graph as in FIG. 86, except for anindication that there is a peak, or second inflection point, that occursat about T=1 hour, especially at low glucose levels, e.g., 100 mg/dL andlower. However, of all the EIS parameters that were studied, membraneresistance was the only one that exhibited a relationship to this changein Isig; the other parameters generally tend to proceed fairly smoothlyto steady state. Thus, as shown in FIG. 89, Rm also exhibits a secondinflection point at about T=1 hour that corresponds to the peak in Isigat the same time.

FIG. 90 shows the relationship between Cal Factor and Rm for in-vivodata during the first 8 hours of sensor operation. Here, EIS was runabout once every 30 minutes at startup, and interpolated for periods inbetween. As can be seen, Rm=Rmem+Rsol correlates with Cal Factor (CF)during the first 8 hours of sensor operation. For purposes of thediagram in FIG. 90, the baseline offset was assumed to be 3 nA.

As noted above in connection with FIGS. 83-85, in one embodiment of theinvention, an algorithm for adjustment of the Cal Factor at start up mayinclude selecting a reference value for the calibration factor(CF_(reference)), estimating the value of membrane resistance(R_(reference)) for CF=CF_(reference), monitoring the change in membraneresistance (Rm=Rmem+Rsol), and based on the magnitude of that change,adjusting the calibration factor in accordance with the relationshipshown in FIG. 90. Thus

CF(t)=CF_(reference) −m(R _(reference) −R _(m)(t))

where m is the gradient of the correlation in FIG. 90. It is noted that,for purposes of the above algorithm, the value of CF_(reference) issensor-specific, to account for the differences between sensors.

In another embodiment, the Cal Factor adjustment algorithm may bemodified by using a limited range of R_(m) over which adjustment occurs.This can help with small differences once R_(m) is smaller than ˜7000Ω,as may happen due to noise. The limited R_(m) range can also help whenR_(m) is very large, as may happen due to very slow sensorhydration/stabilization. In yet another embodiment, the range ofallowable CF may be limited, such as, e.g., by setting a lower limit of4.5 for CF.

FIG. 91A is a chart showing in-vivo results for MARD over all valid BGsin approximately the first 8 hours of sensor life. A single (first)calibration is performed with the first BG at either 1 hour, 1.5 hours,or 2 hours after startup. As can be seen, without any Cal Factoradjustment, the MARD for calibration at 1 hour is much higher than thatfor calibration performed at 2 hours (22.23 vs. 19.34). However, withadjustment, or modified adjustment, as described above, the differencebetween the respective MARD numbers becomes smaller. Thus, for example,with adjustment, the MARD for calibration at 1 hour is 16.98, ascompared to 15.42 for calibration performed at 2 hours. In addition, theMARD with adjustment for calibration at 1 hour is much less than theMARD without adjustment for calibration performed at 2 hours (16.98 vs.19.34). As such, in accordance with embodiments of the invention, CalFactor adjustments (and modified adjustments) may be used to elongatethe useable life of a sensor—e.g., by starting the sensor one hourearlier, in this example—while maintaining, or improving, the MARD. Thechart in FIG. 91B provides median ARD numbers over all valid BGs inapproximately the first 8 hours.

FIGS. 92A-92C, 93A-93C, and 94A-94C show examples of when theabove-described Cal Factor adjustment algorithms work better than somecurrent, non-EIS based, methods. In one such method, generally referredto as “First Day Compensation” (or FDC), a first Cal Factor is measured.If the measured Cal Factor falls outside of a predetermined range, aconstant linear decay function is applied to bring the Cal Factor backto within normal range at a projected time determined by the rate of thedecay. As can be seen from FIGS. 92A-94C, the Cal Factor adjustmentalgorithms of the invention (referred to in the diagrams as“Compensation”) 6701, 6711, 6721 produce results that are closer to theactual blood glucose (BG) measurements 6707, 6717, 6727 than resultsobtained by the FDC method 6703, 6713, 6723.

Given the complexities of estimating the value of EIS-relatedparameters, some of the current methods, including FDC, may becomputationally less complex than the EIS Cal Factor adjustmentalgorithms described herein. However, the two approaches may also beimplemented in a complementary fashion. Specifically, there may besituations in which FDC may be augmented by the instant Cal Factoradjustment algorithms. For example, the latter may be used to define therate of change of the FDC, or to identify the range for which FDC shouldbe applied (i.e., other than using CF alone), or to reverse thedirection of FDC in special cases.

In yet other embodiments, the offset, rather than the Cal Factor, may beadjusted. In addition, or instead, limits may be imposed on applicableranges of R_(m) and CF. In a specific embodiment, absolute, rather thanrelative, values may be used. Moreover, the relationship between CalFactor and membrane may be expressed as multiplicative, rather thanadditive. Thus,

$\frac{{CF}(t)}{{CF}_{reference}} = {- {m\left( \frac{R(t)}{R_{reference}} \right)}}$

In an embodiment using EIS-based dynamic offset, the total current thatis measured may be defined as the sum of the Faradaic current and thenon-Faradaic current, wherein the former is glucose-dependent, while thelatter is glucose-independent. Thus, mathematically,

i _(total) =i _(Faradaic) +i _(non-Faradaic)

Ideally, the non-Faradaic current should be zero, with a fixed workingpotential, such that

$i_{total} = {i_{Faradaic} = {A \times {Diffusivity} \times \frac{\partial C_{peroxide}}{\partial n}}}$

where A is the surface area, and

$\frac{\partial C_{peroxide}}{\partial n}$

is the gradient or Peroxide.

However, when the double layer capacitance in changing, the non-Faradaiccurrent cannot be ignored. Specifically, the non-Faradaic current may becalculated as

q_(non-Faradaic) = V × C = ∫_(t₀)^(t₀ + Δ t)i_(non − Faradaic) d t

where q is the charge, V is the voltage, C is (double layer)capacitance. As can be seen from the above, when both voltage (V) andcapacitance (C) are constant, both time-derivative values on theright-hand side of the equation are equal to zero, such thati_(non-Faradaic)=0. In such an ideal situation, the focus can then turnto diffusion and reaction.

When V and C are both functions of time (e.g., at sensorinitialization),

$i_{{non}\text{-}{Faradaic}} = {\frac{d\left( {V \times C} \right)}{d\; t} = {{C\frac{d\; V}{d\; t}} + {V\frac{d\; C}{d\; t}}}}$

On the other hand, when V is constant, and C is a function of time,

$i_{{non}\text{-}{Faradaic}} = {V\frac{d\; C}{d\; t}}$

Such conditions are present, for example, on day 1 of sensor operation.FIG. 95 shows an example of a typical (initial) decay in double layercapacitance during day 1, in this case, the first 6 hours after sensorinsertion. As indicated on the graph, plot 6805 shows raw Cdl data basedon EIS data obtained at half-hour intervals, plot 6810 shows a splinefit on the raw Cdl data for 5-minute time intervals, plot 6815 shows thesmoothed curve for 5-minute time intervals, and plot 6820 shows apolynomial fit on the smoothed Cdl data for 5-minute time intervals.

It is noted that the Cdl decay is not exponential. As such, the decaycannot be simulated with an exponential function. Rather, it has beenfound that a 6^(th)-order polynomial fit (6820) provides a reasonablesimulation. Thus, for the purposes of the above-mentioned scenario,where V is constant and C is a function of time, i_(non-Faradaic) may becalculated if the polynomial coefficients are known. Specifically,

C=P(1)t ⁶ +P(2)t ⁵ +P(3)t ⁴ +P(4)t ³ +P(5)t ² +P(6)t ¹ +P(7)

where P is the polynomial coefficient array, and t is time. Thenon-Faradaic current can then be calculated as:

$i_{{non}\text{-}{Faradaic}} = {{V\frac{d\; C}{d\; t}} = {V\left( {{6\; {P(1)}\; t^{5}} + {5\; {P(2)}t^{4}} + {4\; {P(3)}t^{3}} + {3\; {P(4)}t^{2}} + {2\; {P(5)}t^{1}} + {P(6)}} \right)}}$

Finally, since i_(total)=i_(Faradaic)+i_(non-Faradaic), the non-Faradaiccomponent of the current can be removed by rearranging, such that

i _(Faradaic) =i _(total) −i _(non-Faradaic)

FIG. 96 shows Isig based on the total current (6840), as a function oftime, as well as Isig after removal of the non-Faradaic current based onthe capacitance decay (6850). The non-Faradaic component of the currentmay be as high as 10-15 nA. As can be seen from the figure, removal ofthe non-Faradaic current helps remove a large majority of the lowstart-up Isig data at the beginning of sensor life.

It has been found that the above approach can be used to reduce theMARD, as well as adjust the Cal Factor right at the beginning of sensorlife. With regard to the latter, FIG. 97A shows the Cal Factor beforeremoval of the non-Faradaic current for a first working electrode (WE1)6860, and a second working electrode (WE2) 6870. FIG. 97B, on the otherhand, shows the Cal Factor for WE1 (6862) and WE2 (6872) after removalof the non-Faradaic current. Comparing the Cal Factor for WE1 in FIG.97A (6860) to that for WE1 in FIG. 97B (6862), it can be seen that, withremoval of the non-Faradaic component, the Cal Factor (6862) is muchcloser to the expected range.

In addition, the reduction in MARD can be seen in the example shown inFIGS. 98A and 98B, where sensor glucose values are plotted over time. Asshown in FIG. 98A, before removal of the non-Faradaic current,calibration at low startup causes significant sensor over-reading at WE1(6880), with a MARD of 11.23%. After removal of the non-Faradaiccurrent, a MARD of 10.53% is achieved for WE1. It is noted that, for theillustrative purposes of FIGS. 97A-98B, the non-Faradaic current wascalculated and removed in pre-processing using the relation

${i_{{non}\text{-}{Faradaic}} = {{V\frac{d\; C}{d\; t}} = {V\left( {{6\; {P(1)}\; t^{5}} + {5\; {P(2)}t^{4}} + {4\; {P(3)}t^{3}} + {3\; {P(4)}t^{2}} + {2\; {P(5)}t^{1}} + {P(6)}} \right)}}},$

where P is the polynomial coefficient (array) used to fit the doublelayer capacitance curve.

In real-time, separation of the Faradaic and non-Faradaic currents maybe used to automatically determine the time to conduct the firstcalibration. FIG. 99 shows the double layer capacitance decay over time.Specifically, over the constant time interval ΔT, the double layercapacitance undergoes a change from a first value C_(T) _(O) _(+ΔT)(7005) to a second value C_(T) (7010). A first-order time differencemethod, e.g., can then be used to calculate the non-Faradaic current as

$i_{{non}\text{-}{Faradaic}} = {{V\frac{d\; C}{d\; t}} \approx {V\frac{C_{T_{0} + {\Delta \; T}} - C_{T}}{\Delta \; T}}}$

Other methods may also be used to calculate the derivative

$\frac{d\; C}{d\; t},$

such as, e.g., second-order accurate finite value method (FVM),Savitzky-Golay, etc.

Next, the percentage of the total current, i.e., Isig, that is comprisedof the non-Faradaic current may be calculated simply as the ratioi_(non-Faradaic)/Isig. Once this ratio reaches a lower threshold, adetermination can then be made, in real-time, as to whether the sensoris ready for calibration. Thus, in an embodiment of the invention, thethreshold may be between 5% and 10%.

In another embodiment, the above-described algorithm may be used tocalculate an offset value in real-time, i.e., an EIS-based dynamicoffset algorithm. Recalling that

$i_{{non}\text{-}{Faradaic}} = {{V\frac{d\; C}{d\; t}} = {V\left( {{6\; {P(1)}\; t^{5}} + {5\; {P(2)}t^{4}} + {4\; {P(3)}t^{3}} + {3\; {P(4)}t^{2}} + {2\; {P(5)}t^{1}} + {P(6)}} \right)}}$

and that sensor current Isig is the total current, including theFaradaic and non-Faradaic components

i _(total) =i _(Faradaic) +i _(non-Faradaic)

the Faradaic component is calculated as

i _(Faradaic) =i _(total) −i _(non-Faradaic)

Thus, in an embodiment of the invention, the non-Faradaic current,i_(non-Faradaic), can be treated as an additional offset to Isig. Inpractice, when double layer capacitance decreases, e.g., during thefirst day of sensor life, i_(non-Faradaic) is negative, and decreases asa function of time. Therefore, in accordance with this embodiment of theinvention, a larger offset—i.e., the usual offset as calculated withcurrent methods, plus i_(non-Faradaic)—would be added to the Isig at thevery beginning of sensor life, and allowed to decay following the5^(th)-order polynomial curve. That is, the additional offseti_(non-Faradaic) follows a 5^(th)-order polynomial, the coefficient forwhich must be determined. Depending on how dramatic the change in doublelayer capacitance is, the algorithm in accordance with this embodimentof the invention may apply to the first few hours, e.g., the first 6-12hours, of sensor life.

The polynomial fit may be calculated in various ways. For example, in anembodiment of the invention, coefficient P may be pre-determined basedupon existing data. Then, the dynamic offset discussed above is applied,but only when the first Cal Factor is above normal range, e.g., ˜7.Experiments have shown that, generally, this method works best when thereal-time double layer capacitance measurement is less reliable thandesired.

In an alternative embodiment, an in-line fitting algorithm is used.Specifically, an in-line double layer capacitance buffer is created attime T. P is then calculated based on the buffer, using a polynomial fitat time T. Lastly, the non-Faradaic current (dynamic offset) at timeT+ΔT is calculated using P at time T. It is noted that this algorithmrequires double layer capacitance measurements to be more frequent thantheir current level (every 30 mins), and that the measurements bereliable (i.e., no artifacts). For example, EIS measurements could betaken once every 5 minutes, or once every 10 minutes, for the first 2-3hours of sensor life.

In developing a real-time, self-calibrating sensor, the ultimate goal isto minimize, or eliminate altogether, the reliance on a BG meter. This,however, requires understanding of the relationships between EIS-relatedparameters and Isig, Cal Factor (CF), and offset, among others. Forexample, in-vivo experiments have shown that there is a correlationbetween Isig and each of Cdl and Warburg Admittance, such that each ofthe latter may be Isig-dependent (at least to some degree). In addition,it has been found that, in terms of factory calibration of sensors, Isigand Rm (=Rmem+Rsol) are the most important parameters (i.e.,contributing factors) for the Cal Factor, while Warburg Admittance, Cdl,and Vcntr are the most important parameters for the offset.

In in-vitro studies, metrics extracted from EIS (e.g., Rmem) tend toexhibit a strong correlation with Cal Factor. However, in-vivo, the samecorrelation can be weak. This is due, in part, to the fact thatpatient-specific, or (sensor) insertion-site-specific, properties maskthe aspects of the sensor that would allow use of EIS forself-calibration or factory calibration. In this regard, in anembodiment of the invention, redundant sensors may be used to provide areference point that can be utilized to estimate the patient-specificresponse. This, in turn, would allow a more robust factory calibration,as well as help identify the source of sensor failure mode(s) as eitherinternal, or external, to the sensor.

In general, EIS is a function of electric fields that form between thesensor electrodes. The electric field can extend beyond the sensormembrane, and can probe into the properties of the (patient's) body atthe sensor insertion site. Therefore, if the environment in which thesensor is inserted/disposed is uniform across all tests, i.e., if thetissue composition is always the same in-vivo (or if the buffer isalways the same in-vitro), then EIS can be correlated to sensor-onlyproperties. In other words, it may be assumed that changes in the sensorlead directly to changes in the EIS, which can be correlated with, e.g.,the Cal Factor.

However, it is well known that the in-vivo environment is highlyvariable, as patient-specific tissue properties depend on thecomposition of the insertion site. For example, the conductivity of thetissue around the sensor depends on the amount of fat around it. It isknown that the conductivity of fat is much lower than that of pureinterstitial fluid (ISF), and the ratio of local fat to ISF can varysignificantly. The composition of the insertion site depends on the siteof insertion, depth of insertion, patient-specific body composition,etc. Thus, even though the sensor is the same, the Rmem that is observedfrom EIS studies varies much more significantly because the referenceenvironment is rarely, if ever, the same. That is, the conductivity ofthe insertion site affects the Rmem of the sensor/system. As such, itmay not be possible to use the Rmem uniformly and consistently as areliable calibration tool.

As described previously, EIS can also be used as a diagnostic tool.Thus, in embodiments of the invention, EIS may be used for gross failureanalysis. For example, EIS can be used to detect severe sensitivity losswhich, in turn, is useful for determining whether, and when, to blocksensor data, deciding on optimal calibration times, and determiningwhether, and when, to terminate a sensor. In this regard, it bearsrepeating that, in continuous glucose monitoring and analysis, two majortypes of severe sensitivity loss are typically considered: (1) Temporarysensitivity loss (i.e., an Isig dip), which typically occurs early insensor life, and is generally believed to be a consequence of externalsensor blockage; and (2) Permanent sensitivity loss, which typicallyoccurs at the end of sensor life, and never recovers, thus necessitatingsensor termination.

Both in-vivo and in-vitro data show that, during sensitivity loss andIsig dips, the EIS parameters that change may be any one or more ofRmem, Rsol, and Cmem. The latter changes, in turn, manifest themselvesas a parallel shift in the higher-frequency region of the Nyquist plot,and/or an increased appearance of the high-frequency semicircle. Ingeneral, the more severe the sensitivity loss, the more pronounced thesesymptoms are. FIG. 100 shows the higher-frequency region of the Nyquistplot for data at 2.6 days (7050), 3.5 days (7055), 6 days (7060), and6.5 days (7065). As can be seen, there may be a horizontal shift, i.e.,Rmem+Rsol shifts, from left to right, during sensitivity loss (7070),indicating an increase in membrane resistance. In addition, the plot for6 days, and especially that for 6.5 days (7065), clearly show theappearance of the higher frequency semicircle during sensitivity loss(7075), which is indicative of a change in membrane capacitance.Depending on the circumstances and the severity of the sensitivity loss,either or both of the above-mentioned manifestations may appear on theNyquist plot.

With specific regard to the detection of Isig dips, as opposed topermanent sensitivity loss, some current methodologies use the Isig onlyto detect Isig dips by, e.g., monitoring the rate at which Isig may bedropping, or the degree/lack of incremental change in Isig over time,thereby indicating that perhaps the sensor is not responsive to glucose.This, however, may not be very reliable, as there are instances whenIsig remains in the normal BG range, even when there is an actual dip.In such a situation, sensitivity loss (i.e., the Isig dip) is notdistinguishable from hypoglycemia. Thus, in embodiments of theinvention, EIS may be used to complement the information that is derivedfrom the Isig, thereby increasing the specificity and sensitivity of thedetection method.

Permanent sensitivity loss may generally be associated with Vcntr rails.Here, some current sensor-termination methodologies rely solely on theVcntr rail data, such that, e.g., when Vcntr rails for one day, thesensor may be terminated. However, in accordance with embodiments of theinvention, one method of determining when to terminate a sensor due tosensitivity loss entails using EIS data to confirm whether, and when,sensitivity loss happens after Vcntr rails. Specifically, the parallelshift in the higher-frequency region of the Nyquist plot may be used todetermine whether permanent sensitivity loss has actually occurred oncea Vcntr rail is observed. In this regard, there are situation in whichVcntr may rail at, e.g., 5 days into sensor life, but the EIS data showslittle to shift at all in the Nyquist plot. In this case, normally, thesensor would have been terminated at 5-6 days. However, with EIS dataindicating that there was, in fact, no permanent sensitivity loss, thesensor would not be terminated, thereby saving (i.e., using) theremainder of the sensor's useful life.

As mentioned previously, detection of sensitivity loss may be based onchange(s) in one or more EIS parameters. Thus, changes in membraneresistance (Rm=Rmem+Rsol), for example, may manifest themselves in themid-frequency (˜1 kHz) real impedance region. For membrane capacitance(Cmem), changes may be manifested in the higher-frequency (˜8 kHz)imaginary impedance because of increased semicircle. The double layercapacitance (Cdl) is proportional to average Isig. As such, it may beapproximated as the length of lower-frequency Nyquist slope L_(nyquist).Because Vcntr is correlated to oxygen levels, normal sensor behaviortypically entails a decrease in Vcntr with decreasing Isig. Therefore,an increase in Vcntr (i.e., more negative), in combination with adecrease in Isig may also be indicative of sensitivity loss. Inaddition, average Isig levels, rates of change, or variability of signalthat are low or physiologically unlikely may be monitored.

The EIS parameters must, nevertheless, be first determined. As describedpreviously in connection with Cal Factor adjustments and relateddisclosure, the most robust way of estimating the EIS parameters is toperform model fitting, where the parameters in model equations arevaried until the error between the measured EIS and the model output areminimized. Many methods of performing this estimate exist. However, fora real time application, model fitting may not be optimal because ofcomputational load, variability in estimation time, and situations whereconvergence is poor. Usually, the feasibility will depend on thehardware.

When the complete model fitting noted above is not possible, in oneembodiment of the invention, one method for real-time application isthrough use of heuristic methodologies. The aim is to approximate thetrue parameter values (or a corresponding metric that is proportional totrends shown by each parameter) with simple heuristic methods applied tothe measured EIS. In this regard, the following are implementations forestimating changes in each parameter.

Double Layer Capacitance (Cdl)

Generally speaking, a rough estimate of Cdl can be obtained from anystatistic that measures the length of the lower-frequency Nyquist slope(e.g., frequencies lower than ˜128 Hz). This can be done, for example,by measuring L_(nyquist) (the Cartesian distance between EIS at 128 Hzand 0.1 Hz in the Nyquist plot). Other frequency ranges may also beused. In another embodiment, Cdl may be estimated by using the amplitudeof the lower-frequency impedance (e.g., at 0.1 Hz).

Membrane Resistance (Rmem) and Solution Resistance (Rsol)

As has been discussed hereinabove, on the Nyquist plot, Rmem+Rsolcorresponds to the inflection point between the lower-frequency and thehigher-frequency semicircles. Thus, in one embodiment, Rmem+Rsol may beestimated by localizing the inflection point by detecting changes indirectionality of the Nyquist slope (e.g., by using derivatives and/ordifferences). Alternatively, a relative change in Rmem+Rsol can beestimated by measuring the shift in the Nyquist slope. To do this, areference point in the imaginary axis can be chosen (see FIG. 83) andinterpolation can be used to determine the corresponding point on thereal axis. This interpolated value can be used to track changes inRmem+Rsol over time. The chosen reference should lie within a range ofvalues that, for a given sensor configuration, are not overly affectedby large changes in the lower-frequency part of the Nyquist slope (forexample, because of Vcntr Rail). Typical values may be between 1 kΩ and3 kΩ. In another embodiment, it may be possible to use the realcomponent of a single high frequency EIS (e.g., 1 kHz, 8 kHz). Incertain sensor configurations, this may simulate Rmem the majority ofthe time, though it is noted that a single frequency may not be able torepresent Rmem exactly in all situations.

Membrane capacitance (Cmem)

Increases in Cmem manifest as a more pronounced (or the more obviousappearance of) a higher-frequency semicircle. Changes in Cmem cantherefore be detected by estimating the presence of this semicircle.Thus, in one embodiment, Cmem may be estimated by tracking thehigher-frequency imaginary component of impedance. In this regard, amore negative value corresponds to the increased presence of asemicircle.

Alternatively, Cmem may be estimated by tracking the highest point inthe semicircle within a frequency range (e.g., 1 kHz-8 kHz). Thisfrequency range can also be determined by identifying the frequency atwhich the inflection point occurs, and obtaining the largest imaginaryimpedance for all frequencies higher than the identified frequency. Inthis regard, a more negative value corresponds to an increased presenceof the semicircle.

In a third embodiment, Cmem may be estimated by measuring the Cartesiandistance between two higher-frequency points in the Nyquist plot, suchas, e.g., 8 kHz and 1 kHz. This is the high frequency slope(S_(nyquist)) defined previously in the instant application. Here, alarger absolute value corresponds to an increased semicircle, and anegative slope (with negative imaginary impedance on the y axis, andpositive real impedance on the x) corresponds to the absence of asemicircle. It is noted that, in the above-described methodologies,there may be instances in which some of the detected changes in thesemicircle may also be attributed to changes in Rmem. However, becausechanges in either are indicative of sensitivity loss, the overlap isconsidered to be acceptable.

Non-EIS Related Metrics

For context, it is noted that, prior to the availability of EIS metrics,sensitivity loss was by and large detected according to several non-EIScriteria. By themselves, these metrics are not typically reliable enoughto achieve perfect sensitivity and specificity in the detection. Theycan, however, be combined with EIS-related metrics to provide supportingevidence for the existence of sensitivity loss. Some of these metricsinclude: (1) the amount of time that Isig is below a certain threshold(in nA), i.e., periods of “low Isig”; (2) the first order or secondorder derivatives of Isig leading to a state of “low Isig”, used as anindication of whether the changes in Isig are physiologically possibleor induced by sensitivity loss; and (3) the variability/variance of Isigover a “low Isig” period, which can be indicative of whether the sensoris responsive to glucose or is flat lining.

Sensitivity-Loss Detection Algorithms

Embodiments of the invention are directed to algorithms for detection ofsensitivity loss. The algorithms generally have access to a vector ofparameters estimated from EIS measurements (e.g., as describedhereinabove) and from non-EIS related metrics. Thus, e.g., the vectormay contain Rmem and or shift in horizontal axis (of the Nyquist plot),changes in Cmem, and changes in Cdl. Similarly, the vector may containdata on the period of time Isig is in a “low” state, variability inIsig, rates of change in Isig. This vector of parameters can be trackedover time, wherein the aim of the algorithm is to gather robust evidenceof sensitivity loss. In this context, “robust evidence” can be definedby, e.g., a voting system, a combined weighted metric, clustering,and/or machine learning.

Specifically, a voting system may entail monitoring of one or more ofthe EIS parameters. For example, in one embodiment, this involvesdetermining when more than a predetermined, or calculated, number of theelements in the parameter vector cross an absolute threshold. Inalternative embodiments, the threshold may be a relative (%) threshold.Similarly, the vector elements may be monitored to determine when aparticular combination of parameters in the vector crosses an absoluteor a relative threshold. In another embodiment, when any of a subset ofelements in the vector crosses an absolute or a relative threshold, acheck on the remainder of the parameters may be triggered to determineif enough evidence of sensitivity loss can be obtained. This is usefulwhen at least one of a subset of parameters is a necessary (but perhapsinsufficient) condition for sensitivity loss to be reliably detected.

A combined weighted metric entails weighing the elements in the vectoraccording to, for example, how much they cross a predetermined thresholdby. Sensitivity loss can then be detected (i.e., determined asoccurring) when the aggregate weighted metric crosses an absolute or arelative threshold.

Machine learning can be used as more sophisticated “black box”classifiers. For example, the parameter vector extracted from realisticin-vivo experimentation can be used to train artificial neural networks(ANN), support vector machines (SVM), or genetic algorithms to detectsensitivity loss. A trained network can then be applied in real time ina very time-efficient manner.

FIGS. 101A and 101B show two illustrative examples of flow diagrams forsensitivity-loss detection using combinatory logic. As shown, in bothmethodologies, one or more metrics 1-N may be monitored. In themethodology of FIG. 101A, each of the metrics is tracked to determine ifand when it crosses a threshold, and described hereinabove. The outputof the threshold-determination step is then aggregated via a combinatorylogic, and a decision regarding sensitivity loss is made based on theoutput of the combinatory logic. In FIG. 101B, values of the monitoredmetrics 1-N are first processed through a combinatory logic, and theaggregate output of the latter is then compared to a threshold value(s)to determine whether sensitivity loss has occurred.

Additional embodiments of the invention are also directed to using EISin intelligent diagnostic algorithms. Thus, in one embodiment, EIS datamay be used to determine whether the sensor is new, or whether it isbeing re-used (in addition to methodologies presented previously inconnection with re-use of sensors by patients). With regard to thelatter, it is important to know whether a sensor is new or is beingre-used, as this information helps in the determination of what type ofinitialization sequence, if any, should be used. In addition, theinformation allows prevention of off-label use of a sensor, as well asprevention of sensor damage due to multiple reinitializations (i.e.,each time a sensor is disconnected and then re-connected, it “thinks”that it is a new sensor, and therefore tries to reinitialized uponre-connection). The information also helps in post-processing ofcollected sensor data.

In connection with sensor re-use and/or re-connection, it has beendiscovered that the lower-frequency Nyquist slope for a new sensorbefore initialization is different from (i.e., lower than) thelower-frequency Nyquist slope for a sensor that has been disconnected,and then reconnected again. Specifically, in-vitro experiments haveshown that the Nyquist slope is higher for a re-used sensor as opposedto a newly-inserted one. The Nyquist slope, therefore, can be used as amarker to differentiate between new and used (or re-used) sensors. Inone embodiment, a threshold may be used to determine, based on theNyquist slope, whether a specific sensor is being re-used. Inembodiments of the invention, the threshold may be a Nyquist slope=3.FIG. 102 shows the low-frequency Nyquist plot with a reference slope=3(8030), as well as the plots for a new sensor (pre-initialization) 8010,a new sensor (post-initialization) 8015, a reconnected sensor(pre-initialization) 8020, and a reconnected sensor(post-initialization) 8020. As noted, the slope for a new sensor(pre-initialization) 8010 is lower than the reference, or threshold(8030), while that for a reconnected sensor (pre-initialization) 8020 ishigher than the threshold (8030).

Equivalently, lower-frequency phase measurements may be used to detectsensors that have been previously initialized. Here, thepre-initialization phase angle at 0.105 Hz, e.g., may be used todifferentiate between new and used (or re-used) sensors. Specifically, athreshold may be set at a phase angle of about −70°. Thus, if thepre-initialization phase angle at 0.105 Hz is less than the threshold,then the sensor is considered to be an old (i.e.,previously-initialized) sensor. As such, no further initializationpulses will be applied to the sensor.

In another embodiment, EIS data may be used to determine the type ofsensor being used. Here, it has been discovered that, if the sensordesigns are significantly different, the respective EIS outputs shouldalso be significantly different, on average. Different sensorconfigurations have different model parameters. It is therefore possibleto use identification of these parameters at any point during the sensorlife to determine the sensor type currently inserted. The parameters canbe estimated, e.g., based on methods described hereinabove in connectionwith gross failure/sensitivity-loss analysis. Identification can bebased on common methods to separate values, for example, settingthresholds on specific (single or multiple) parameters, machine learning(ANN, SVM), or a combination of both methods.

This information may be used, e.g., to change algorithm parameters andinitialization sequences. Thus, at the beginning of the sensor life,this can be used to have a single processing unit (GST, GSR) to setoptimal parameters for the calibration algorithm. Offline (nonreal-time), the identification of sensor type can be used to aidanalysis/evaluation of on-the-field sensor performance.

It has also been discovered that the length of the lower-frequencyNyquist slope may be used to differentiate between different sensortypes. FIGS. 103A-103C show Nyquist plots for three different sensors(i.e., different sensor configurations), identified as Enlite (8050),Enlite 2 (i.e., “Enlite Enhanced”) (8060), and Enlite 3 (8070), all ofwhich are manufactured by Medtronic Minimed (Northridge, Calif.). As canbe seen, for various stages, including pre-initialization,post-initialization, and second post-initialization (FIGS. 103A-103C,respectively), the Enlite sensor has the shortest lower-frequencyNyquist slope length (8050), followed by the Enlite 2 (8060), and theEnlite 3 (8070), which has the longest length. The latter are also shownon FIG. 104, where Nyquist (slope) length, computed as the Cartesiandistance between EIS at 0.105 Hz and 1 Hz, is plotted against time.

Embodiments of the invention are also directed to using diagnostic EISmeasurements as a guide in determining the type of initialization thatshould be performed. As noted previously, initialization sequences canbe varied based on detected sensor type (EIS-based or other), and/ordetection of whether a new or old sensor is inserted (EIS-based). Inaddition, however, EIS-based diagnostics may also be used in determininga minimal hydration state prior to initialization (e.g., by trackingWarburg impedance), or in determining when to terminate initialization(e.g., by tracking reaction-dependent parameter, such as, e.g., Rp, Cdl,Alpha, etc.), so as to properly minimize sensor initialization time.

More specifically, to minimize initialization response time, additionaldiagnostics are required to control the processes that occur duringinitialization. In this regard, EIS may provide for the requiredadditional diagnostics. Thus, for example, EIS may be measured betweeneach initialization pulse to determine if further pulsing is required.Alternatively, or in addition, EIS may be measured during high pulses,and compared to the EIS of optimal initialization state to determinewhen the sensor is sufficiently initialized. Lastly, as noted above, EISmay be used in estimating a particular model parameter—most likely oneor more reaction-dependent parameters, such as Rp, Cdl, Alpha, etc.

As has been noted, sensor calibration in general, and real-time sensorcalibration in particular, is central to a robust continuous glucosemonitoring (CGM) system. In this regard, calibration algorithms aregenerally designed such that, once a BG is received by taking afingerstick, the new BG value is used to either generate an errormessage, or update the calibration factor which, in turn, is used tocalculate sensor glucose. In some previous algorithms, however, a delayof 10-20 minutes may exist between the time when a fingerstick isentered, and the time when the user is notified of either thefingerstick being accepted or a new fingerstick being required forcalibration. This is burdensome, as the user is left not knowing whetherhe/she will need his/her BG meter again in a few minutes.

In addition, in some situations, the presence of older BG values in thecalibration buffer causes either perceived system delay, due to thenewest BG value carrying less than 100% weight, or inaccuracy in thecalculated SG (due to the older BG values no longer being representativeof the current state of the system). Moreover, erroneous BG values aresometimes entered, but not caught by the system, which may lead to largeinaccuracies until the next calibration.

In view of the above, embodiments of the invention seek to addresspotential shortcomings in prior methodologies, especially with regard tosensor performance for use with closed-loop systems. For example, inorder to make the system more predictable, calibration errors may benotified only when the fingerstick (BG value) is received by thetransmitter (i.e., entered), rather than, e.g., 10-15 minutes later.Additionally, in contrast to some existing systems, where a constantcalibration error (CE) threshold is used, embodiments of the inventionmay utilize variable calibration error thresholds when higher errors areexpected (e.g., either due to lower reliability of the sensor, or highrates of change), thereby preventing unnecessary calibration erroralarms and fingerstick requests. Thus, in one aspect, when the sensor isin FDC mode, Isig dip calibration mode, or undergoing a high rate ofchange (e.g., when 2-packet rate of change× CF>1.5 mg/dL/min.), a limitcorresponding to 50% or 50 mg/dL may be used.

On the other hand, when low error is expected, the system may use atighter calibration error limit, such as, e.g., 40% or 40 mg/dL. Thisreduces the likelihood that erroneous BG values may be used forcalibration, while also allowing the status of the calibration attemptto be issued immediately (i.e., accepted for calibration, or acalibration error). Moreover, in order to handle situations where newerIsig values would cause a calibration error, a check at calibration time(e.g., 5-10 minutes after fingerstick) may select the most appropriatefiltered Isig (fIsig) value to use for calibration.

In connection with the aforementioned issues involving BG values and theBG buffer, embodiments of the invention aim to reduce the delay, and theperceptions of delay, by assigning higher weighting to the newer BGvalue than was assigned in previous algorithms, and by ensuring that theearly calibration update occurs more frequently. In addition, insituations where there is a confirmed sensitivity change (as confirmed,e.g., by the Smart Calibration logic mentioned previously and to beexplored hereinbelow, and by recent calibration BG/Isig ratios), thecalibration buffer may undergo partial clearing. Lastly, whereas prioralgorithms may have employed an expected calibration factor (CF) weightwhich was a constant, embodiments of the invention provide for avariable CF value based on sensor age.

In short, embodiments of the invention provide for variable calibrationerror thresholds based on expectation of error during calibrationattempt, as well as issuance of calibration error message(s) withoutwaiting for additional sensor data, less delay in calibrating (e.g.,5-10 minutes), updated expected calibration factor value based on sensorage, and partial clearing of the calibration buffer as appropriate.Specifically, in connection with First Day Compensation (FDC),embodiments of the invention provide for requesting additionalcalibrations when higher Cal Factor thresholds are triggered in order tomore expeditiously correct sensor performance. Such higher CF thresholdsmay be set at, e.g., between 7 and 16 mg/dL/nA, with the latter servingas the threshold for indication of calibration error in embodiments ofthe invention.

Thus, in one aspect, if a high CF threshold is triggered after the firstcalibration, the system requires that the next calibration be performedin 3 hours. However, if a high CF threshold is triggered after thesecond, or subsequent, calibration, the system requires that the nextcalibration be performed in 6 hours. The foregoing procedure may beimplemented for a period of 12 hours from sensor connection.

In another aspect, the expected Cal Factor, which is used duringcalibration to calculate the Cal Factor, is increased over time so as toreduce the likelihood of under-reading. By way of background, existingmethodologies may use a fixed expected Cal Factor throughout the sensorlife, without accounting for possible shifts in sensor sensitivity. Insuch methodologies, the expected Cal Factor may be weighted incalculating the final Cal Factor, and used to reduce noise.

In embodiments of the present invention, however, the expected CF iscalculated as a function of time, expressed in terms of the age of thesensor. Specifically,

${{Expected}\mspace{14mu} {CF}} = {{{SensorAge} \times \frac{0.109\mspace{14mu} {{{mg}/{dL}}/{nA}}}{day}} + {4.730\mspace{14mu} {{{mg}/{dL}}/{nA}}}}$

where Sensor Age is expressed in units of days. In further embodiments,the expected Cal Factor may be calculated as a function of the existingCF and impedance, such that any changes in sensitivity may be reflectedin the expected CF. In addition, in aspects of the invention, expectedCF may be calculated on every Isig packet, rather than doing so only ata BG entry, so as to gradually adjust the Cal Factor betweencalibrations.

In connection with calibration buffer and calibration errorcalculations, embodiments of the invention provide for modification ofcalibration buffer weights and/or clearing of the calibration buffer.Specifically, when impedance measurements (e.g., through EIS) indicatethat the Cal Factor might have changed, and a calibration attemptindicates that a change might have occurred, the change in Cal Ratio(CR) is checked by comparing the CR of the current BG to the most recentCR in the calibration buffer. Here, such a change may be verified by,e.g., values of the 1 kHz impedance, as detailed previously inconnection with related EIS procedures. In addition, weights may beadded in the calibration buffer calculation based on reliabilityindices, the direction in which the Cal Factor is expected to change,and/or the rate of change of calibration. In the latter situation, e.g.,a lower weight may be assigned, or CF only temporarily updated, ifcalibration is on a high rate of change.

In embodiments of the invention, selection of filtered Isig (fIsig)values for the calibration buffer may be initiated on the second Isigpacket after BG entry. Specifically, the most recent of the past three(3) fIsig values that would not cause a calibration error may beselected. Then, once accepted for calibration, the calibration processwill proceed without a calibration error being issued. Such calibrationerror may be caused, e.g., by an invalid Isig value, a Cal Ratio rangecheck, a percentage error check, etc.

In other embodiments, values of fIsig may be interpolated to derive aone minute resolution. Alternatively, fIsig values may be selected fromrecent values based on the rate of change in the values (and accountingfor delays). In yet another alternative embodiment, fIsig values may beselected based on a value of CR that is closest to a predicted CR value.The predicted CR value, in turn, is closest to the current value of theCal Factor, unless the latter, or EIS data, indicate that CF shouldchange.

As noted previously, in connection with FIGS. 24 and 34, e.g., valuesfor 1 kHz real impedance provide information on potential occlusion(s)that may exist on the sensor membrane surface, which occlusion(s) maytemporarily block passage of glucose into the sensor and thus cause thesignal to dip. More broadly, the 1 kHz real impedance measurement may beused to detect sensor events that are typically sudden, and may indicatethat the sensor is no longer fully inserted. In this regard, FIG. 105shows a flow chart for a method of blanking sensor data or terminatingthe sensor in accordance with an embodiment of the invention.

The methodology starts at block 9005, where 1 kHz real impedance valuesare filtered using, e.g., a moving average filter, and, based thereon, adetermination is made as to whether the EIS-derived values are stable(9010). If it is determined that the EIS-derived values are not stable,the methodology proceeds to block 9015, wherein a further determinationis made based on the magnitude of the 1 kHz impedance. Specifically, ifboth the filtered and unfiltered values of 1 kHz real impedance are lessthan 7,000Ω, then EIS is set as stable (9020). If, on the other hand,both the filtered and unfiltered values of 1 kHz real impedance are notless than 7,000Ω, then EIS is set as unstable (9025). It is noted thatthe above-described 7,000Ω threshold prevents data blanking or sensortermination for sensors that have not stabilized.

When EIS is stable, the algorithm proceeds to block 9030. Here, if the 1kHz real impedance is less than 12,000Ω (9030), and also less than10,000Ω (9040), the algorithm determines that the sensor is withinnormal operating range and, as such, allows sensor data to continue tobe displayed (9045). If, on the other hand, the 1 kHz real impedancevalue is greater than 10,000Ω (i.e., when the 1 kHz real impedance isbetween 10 kΩ and 12 kΩ), the logic determines whether the 1 kHz realimpedance value has been high (i.e., greater than 10 kΩ) for the past 3hours (9050). If it is determined that the 1 kHz real impedance valuehas been high for the past 3 hours, then the sensor is terminated at9060, as the sensor is assumed to have pulled out, rendering sensor datainvalid. Otherwise, the sensor is not terminated, as the sensor signalmay be simply drifting, which, as discussed previously, may be arecoverable phenomenon. Nevertheless, the sensor data is blanked (9055)while the sensor is given a chance to recover.

It is noted that, in further embodiments, in determining whether datashould be blanked, or the sensor terminated, the logic may alsoconsider, in addition to the above-mentioned thresholds, suddenincreases in impedance by, e.g., comparing impedance derivatives tohistorical derivatives. Moreover, the algorithm may incorporatenoise-based blanking or termination, depending on the duration of highnoise-low sensor signal combination. In this regard, prior methodologiesincluded termination of the sensor after three (3) consecutive 2-hourwindows of high noise and low sensor signal. However, in order toprevent unreliable data from being displayed to the user, embodiments ofthe invention employ noise-based blanking, wherein the algorithm stopscalculating SG values after 2 consecutive 2-hour windows (i.e., at thestart of the third consecutive window) involving high noise and lowsignal. In further aspects, the algorithm may allow further calculationand display of the calculated SG values after one hour of blanking,rather than two hours, where the sensor signal appears to haverecovered. This is an improvement over methodologies that blankotherwise reliable data for longer periods of time.

Whereas 1 kHz real impedance may be used to detect sudden sensorfailures, measurements of imaginary impedance at higher frequencies(e.g., 8 kHz) may be used to detect more gradual changes, where sensorsensitivity has drifted significantly from its typical sensitivity. Inthis regard, it has been discovered that a large shift in 8 kHzimaginary impedance typically signifies that the sensor has experienceda large change in glucose sensitivity, or is no longer stable.

FIG. 106 shows a flow diagram for a method of sensor termination inaccordance with an embodiment of the invention. As shown in FIG. 106,the algorithm employs a reference at 1.5 days (since sensor start), asdoing so provides for a more robust logic, and ensures that the logicfocuses on long-term sensitivity changes. Thus, if the sensor has notbeen operating for at least 1.5 days (9002), no action is taken, and thealgorithm “waits” (9012), i.e., it periodically loops back to step 9002.Once the condition in block 9002 is met, a determination is made as towhether a reference imaginary impedance value is set (9022). If areference value has not been previously set, the algorithm proceeds toset one by assigning the minimum 8 kHz imaginary impedance value sincesensor initialization as the reference value (9032), clipped within therange −1,000Ω-800Ω. With the reference value set, a change value iscalculated as the absolute value of the difference between the referencevalue and the current value of the 8 kHz imaginary impedance (9052). Inblock 9062, the algorithm determines whether the change value is greaterthan 1,200Ω for two consecutive measurements, as well as whether the CalRatio is larger than 14. If at least one of the latter inquiries isanswered in the negative, then the sensor is allowed to continueoperating and display SG values (9072). However, if the change value isgreater than 1,200Ω for two consecutive measurements, and the Cal Ratiois larger than 14, then the sensor is terminated at block 9082.

Embodiments of the invention are also directed to assessment ofreliability of sensor glucose values, as well as estimation ofsensor-data error direction, in order to provide users and automatedinsulin delivery systems—including those in closed-loop systems—anindicator of how reliable the system is when SG is displayed to theuser. Depending on the reliability of sensor data, such automatedsystems are then able to assign a corresponding weight to the SG, andmake a determination as to how aggressively treatments should beprovided to users. Additionally, the direction of error can also be usedto inform users and/or the insulin delivery system in connection with SGbeing a “false low” or a “false high” value. The foregoing may beachieved by, e.g., detecting dips in sensor data during the first day(EIS dip detection), detecting sensor lag, and lower-frequency (e.g., 10Hz) impedance changes.

Specifically, in accordance with an embodiment of the invention, it hasbeen discovered that a Cal Factor (CF) of above about 9 mg/dL/nA may beindicative of low sensor reliability and, as such, a predictor of highererror. Thus, CF values outside of this range may be generally indicativeof one or more of the following: abnormal glucose sensitivity;calibrations that occurred during a dip in signal; delay in entering BGinformation, or high rate of change when calibrating; BG error whencalibrating; and sensor with a transient change in glucose sensitivity.

FIG. 107 shows a flow diagram for a signal dip detection methodology inaccordance with an embodiment of the invention, where increases inunfiltered real 1 kHz impedance may be used in combination with low Isigvalues to identify the start of a dip. As shown in the diagram, at block9102, the logic determines whether sensor data is currently beingblanked due to signal dip. If data is not being blanked, then the logicdetermines whether less than 4 hours have passed since sensor start(9104). If more than 4 hours have elapsed since sensor start, the logicthen determines whether more than 12 hours have passed since sensorstart (9106), in which case there will be no dip detection or blankingof data (9108). Thus, in this regard, the methodology is directed toidentifying transient dips during the first 12 hours of sensor data.

Returning to block 9106, if less than 12 hours have passed since sensorstart, then an inquiry is made regarding the recent EIS, Isig, and SGvalues. Specifically, in block 9110, if the two most-recent realimpedance values (at 1 kHz) have been increasing, Isig<18 nA, and SG<80mg/dL, then the algorithm determines that the start of a dip has beendetected, and notifies the system to stop displaying SG values (9112).On the other hand, if all of the foregoing conditions are not met, thenthere will be no dip detection or data blanking (9108).

When it is determined, at block 9104, that less than 4 hours have passedsince sensor start, then a sensor dip event may still be encountered.Specifically, if the two most-recent EIS (i.e., 1 kHz impedance) valuesare increasing, and Isig<25 nA, then the algorithm determines that thestart of a dip has been detected, and notifies the system to stopdisplaying SG values (9114, 9116). If, however, the two most-recent 1kHz impedance values are not increasing, or Isig is not less than 25 nA,then there will be no dip detection or data blanking (9108), as before.

Returning to block 9102, if it is determined that data is currentlybeing blanked due to a dip, there is still a possibility that data willnevertheless be shown. That is, if Isig is greater than about 1.2 timesIsig at the start of the dip event (9118), then it is determined thatIsig has recovered, i.e., the dip event is over, and data display willresume (9122). On the other hand, if Isig is not greater than about 1.2times Isig at the start of the dip event (9118), then it is determinedthat Isig has not yet recovered, i.e., the dip event is not over, andthe system will continue to blank sensor data (9120).

In accordance with embodiments of the invention, the direction of errorin SG (under-reading or over reading), in general, may be determined byconsidering one or more factors related to under- and/or over-reading.Thus, it has been discovered that under-reading in sensors may occurwhen: (1) Vcntr is extreme (e.g., Vcntr<−1.0 V); (2) CF is high (e.g.,CF>9); (3) lower frequency impedance (e.g., at 10 Hz) is high (e.g.,real 10 Hz impedance>10.2 kΩ); (4) FDC is in low CF mode; (5) sensor lagsuggests under-reading; (6) lower frequency impedance (e.g., at 10 Hz)increases (e.g., 10 Hz impedance increases over 700Ω); and/or (7) EIShas detected a dip. Over-reading, on the other hand, may occur when: (1)lower frequency impedance (e.g., 10 Hz) decreases (e.g., lower frequencyimpedance<−200Ω); (2) sensor lag suggests over-reading; and/or (3) FDCwhen CF is in extreme mode.

Such under-reading or over-reading, especially in closed-loop systems,can have a profound impact on patient safety. For example, over-readingnear the hypoglycemic range (i.e., <70 mg/dL) may cause an overdose ofinsulin to be administered to the patient. In this regard, severalindicators of error direction have been identified, which may be used astest criteria, including: (1) low sensitivity indicators; (2) sensorlag; (3) FDC mode; and (4) loss/gain in sensitivity since calibration.

Two such low sensitivity indicators are high (lower-frequency) realimpedance (e.g., >10 kΩ) and high Vcntr (e.g., Vcntr<−1.0V), both ofwhich are, in general, indicative of loss of sensitivity. FIG. 108Ashows an example in which Vcntr 9130 gradually increases (i.e., becomemore negative) as a function of time. At about 115 hours, shown by line9135, Vcntr crosses −1.0V, as indicated by line 9137, and continues toincrease (i.e., Vcntr<−1.0V) to about −1.2V. As shown, prior to about115 hours, the Isig trend 9132 generally follows the Vcntr trend.However, once Vcntr passes the threshold (i.e., to the right of line9135), the Isig departs from Vcntr, and continues to drop. At the sametime, as shown in FIG. 108B, glucose 9134 also has a generally downwardtrend, with Cal errors 9136 being indicated at about 130 hours and about165 hours.

As discussed previously, (EIS) sensor dips are also indicative oftemporary sensitivity loss. Similarly, a high Cal Factor is indicativeof the sensor's attempt to compensate for reduced sensitivity. In oneexample shown in FIGS. 109A and 109B, the Cal Factor 9140 increasessteadily as a function of time. At about 120 hours (9145), the CalFactor 9140 crosses a threshold value of 9 (9147). As shown in FIG.109B, once the Cal Factor crosses the threshold, the glucose values 9142show more frequent departures from BG values, with several errors 9144occurring between about 135 hours and 170 hours.

As mentioned previously, sensor lag is another indicator of errordirection. Accordingly, in an embodiment of the invention, the errorthat is caused by sensor lag is compensated for by approximating whatthe glucose value will be. Specifically, in an embodiment of theinvention, the error from sensor lag may be approximated by defining:

sg(t+h)=sg(t)+hsg′(t)+½h ² sg″(t)

where sg(t) is the sensor glucose function, and “h” is the sensor lag.The error may then be calculated as

${Error} = {\frac{{{sg}\left( {t + h} \right)} - {{sg}(t)}}{{sg}(t)} = \frac{\left( {{{hsg}^{\prime}(t)} + {\frac{1}{2}h^{2}{{sg}^{''}(t)}}} \right)}{{sg}(t)}}$or  ${Error} = {\frac{k\left( {{C_{1}{{sg}^{\prime}(t)}} + {C_{2}{{sg}^{''}(t)}}} \right)}{{sg}(t)}.}$

First day calibration (FDC) occurs when the Cal Factor (CF) is notwithin the expected range. The CF is set to the value indicated by thecalibration, and then ramps up or down to the expected range, as shown,e.g., in FIGS. 110A and 110B. During this time, usually high, butgenerally predictable, errors may exist, resulting in potentialover-reads or under-reads. As can be seen from FIGS. 110A and 110B, theCF changes at a generally constant slope as it rises or falls, and thensettles, in this case at 4.5 or 5.5.

Lastly, post-calibration sensitivity change, i.e., loss/gain insensitivity since calibration, is also an indicator of error/errordirection. Under normal circumstances, and except for first daycalibration as discussed hereinabove, the Cal Factor remains generallyconstant until a new calibration is performed. Shifts in sensitivityafter calibration, therefore, can cause over-reads and under-readswhich, in turn, may be reflected by values of lower-frequency (e.g., 10Hz) real impedance.

Specifically, it has been discovered that a drop in lower-frequency realimpedance causes over-reading, with the direction of error beingindicated by the real impedance curve. Conversely, lower-frequencyreal-impedance increases cause under-reading, with the direction oferror also being indicated by the real impedance curve. However, currentdirectionality tests may be unable to readily decipher points at peaksand valleys of the glucose profile. Thus, in one embodiment, the degreeof sharpness of such peaks and valleys may be reduced by filtering, suchas, e.g., by deconvolution with lowpass filtering.

As described previously in connection with FIG. 81, e.g., sensitivitychange and/or loss may be used to inform proper sensor calibration. Inthis regard, in a further aspect of the invention, changes in sensorsensitivity may be predicted based on the previous calibration factor oron impedance so as to enable implementation of “smart calibrations”,which help address continued generation and/or display of inaccurateglucose data when, e.g., sensor sensitivity has changed.

It is known that, in some existing continuous glucose monitoring systems(CGMS), calibration fingersticks are required every twelve hours. Thecalibration allows the CGMS to update the function used to convert themeasured sensor current into a displayed glucose concentration value. Insuch systems, the 12-hour calibration interval is selected as a balancebetween reducing the user burden (of performing too many fingersticks)and using an interval that is sufficient to adjust for changes in sensorsensitivity before inaccuracies can cause too large of a problem.However, while this interval may be appropriate in general, if thesensor sensitivity has changed, 12 hours can be too long to wait if ahigh level of accuracy (in support of closed loop insulin delivery) isexpected.

Embodiments of the invention, therefore, address the foregoing issues byusing the previous calibration factor (see discussion of FDC below), orimpedance (see discussion of EIS-based “smart calibrations” below), topredict if sensitivity has changed. Aspects of the invention also usetime limits to maintain predictability for users, as well as includesteps (in the associated methodology) to ensure that detection is robustto variations between sensors.

FIG. 111 shows a flow diagram in accordance with an embodiment of theinvention for First Day Calibration (FDC). Starting at block 9150, ifFDC is not on after successful calibration, there is simply no smartcalibration request (9151). However, if FDC is on, a determination ismade at block 9153 as to whether this is the first calibration and, ifit is not, then a smart calibration request is made, with the timer setfor 6 hours, i.e., it is requested that an additional calibration bemade in 6 hours (9155). If, on the other hand, this is the firstcalibration, then block 9157 determines whether the Cal Ratio is lessthan 4, or greater than 7. If the condition in block 9157 is not met,then the logic proceeds to block 9155 where, as noted above, a smartcalibration request is made, with the timer set for 6 hours. However, ifthe criterion in block 9157 is not met, then a smart calibration requestis made, with the timer set for 3 hours, i.e., it is requested that anadditional calibration be made in 3 hours (9159). Thus, in order toimprove accuracy for sensors which need calibration adjusted, additional(smart) calibrations are requested which, in turn, limit the amount oftime where the adjustment is incorrect.

In contrast with FDC mode, EIS-based smart calibration mode provides foradditional calibrations if impedance changes. Thus, in an embodiment ofthe invention shown in FIG. 112, an allowed range relating to impedancevalues (and as defined hereinbelow) is set in the hour after calibrationand, following the calibration, a request for additional calibrations ismade if impedance is outside of range. Thus, if not within one hoursince calibration, a determination is made as to whether the filtered 1kHz imaginary impedance value is outside of range (9160, 9162). If theimpedance value is not outside of range, then no change is made (9164).However, if the filtered 1 kHz imaginary impedance value is outside ofrange, then the calibration timer is updated so that calibration isrequested to be performed at 6 hours from the previous calibration(9168). It is noted that, while higher-frequency imaginary impedancetends to better identify changes in glucose sensitivity, towards thehigher end of the frequency spectrum, measurements are generally noisierand, as such, may require filtering.

Returning to block 9160, if it is determined that less than one hour haspassed since calibration, then the range for impedance values may beupdated (9166). Specifically, in one embodiment, the impedance rangecalculation is performed on the last EIS measurement 1 hour aftercalibration. In a preferred embodiment, the range is defined as

range=3×median(|x _(i) −x _(j)|)

where j is the current measurement, and i are the most recent 2 hours ofvalues. In addition, the range may be limited to be values between 50Ωand 100Ω. It is noted that the range as defined above allows for 3 timesmedian value. The latter has been discovered to be more robust than the2-standard-deviation approach used in some prior algorithms, whichallowed noise and outliers to cause inconsistencies.

Embodiments of the invention for continuous glucose monitoring (CGM) arealso directed to using Kalman filters for sensor calibration,independently of the actual design of the subject sensor(s). As notedpreviously, sensor calibration generally involves determination of a CalFactor (CF) based on a reference blood glucose (BG), the associatedIsig, and an offset value. The BG and Isig, in turn, may include noise,and the offset may be sensor (design)-specific, such that the Cal Factoris also sensor-specific. It has been discovered, however, that byutilizing an Unscented Kalman filter, an underlying calibrationmethodology may be developed that is sensor-unspecific, so long as thesensor is linear. Thus, a single calibration methodology (and relatedsystems) may be used to calibrate various sensors, without the need tore-calculate a calibration factor and/or an offset value for eachspecific sensor, and without the need to design a (separate) filteringmechanism to compensate for noise. In this way, both Cal Factor andoffset can be allowed to change over time without the need to change thecodebase on which the calibration algorithm otherwise operates.

In this regard, it is known that, every time a new glucose sensor isdeveloped, there is a need to re-evaluate and re-generate themethods/algorithms used for calibration. As part of such re-evaluation,assumptions, as well as constants, must be re-defined for each newsensor design. In addition, the mathematics in the calibrationmethodology is, in general, heuristically (and manually) reviewed. As isdescribed in detail hereinbelow, however, use of the unscented Kalmanfilter provides for a calibration methodology, wherein the onlyassumption is that the sensor is linear (although other, includingnon-linear, relationships may also be accommodated by modified versionsof the instant invention). This, in turn, provides a significantadvantage, as the invented methodology can be applied to any new linearsensor, thereby significantly reducing development times for newsensors.

In existing methodologies, where the relationship between Isig and BG isgenerally assumed to be linear, the calibration factor (for a singleworking electrode, WE) may be calculated as

CF=BG/(Isig+offset)

Given that, typically, there is noise in the reference BG as well as inthe Isig, some filtering may be applied so that several BGs can beaveraged over time, and/or using complex functions of BG level, therebyproviding more robust calibration. The sensor glucose value (SG) maythen be calculated as

SG=CF×(Isig+offset)

More specifically, as has been noted, a periodic sensor measurement (SG)may be represented by the following relation

SG=CF(Isig+offset)+ε_(s)

where “Isig” denotes the physical output of the sensor (current in nA),and “CF” represents the calibration factor that relates the glucoselevel to the measured output. The calibration factor is not knownprecisely and varies over time; as such, it is estimated and compensatedin real time. The sensor bias is represented by “offset”, which is atime variant variable, and random sensor error is represented by ε_(s).The latter is completely random and, as such, cannot be estimated.

Blood glucose (BG) level is measured using the finger stick, e.g., via ameter. A general BG measurement differs from SG by a random error(ε_(B)), i.e.,

SG=BG+ε_(B)

There is also a first order lag between sensor glucose measurements (SG)and physical output (Isig). Thus,

$\overset{.}{SG} = {{{- \frac{1}{\tau}}{SG}} + {\frac{1}{\tau}({Isig})}}$

where τ is time constant that defines the dynamic relationship betweenSG and Isig. In the above relationship, τ is not known precisely, andcan vary by patient, sensor location, time, and and/or other variables.Assuming that the time constant is constant (e.g., ⅙h=10 min), a dynamicvariable may be established which can be treated as an uncertainparameter that is then estimated and compensated using a Kalman filter.

Generally speaking, a Kalman filter is an optimal estimator that uses aseries of measurements containing noise and produces statisticallyoptimal estimates of unknown variables. It is recursive, such that newmeasurements can be processed as they arrive to update the estimates.While Kalman filters, in general, require linearization ordiscretization of the underlying equations that describe the state ofthe system being evaluated, an Unscented Kalman Filter deals directlywith any such nonlinearity in the measurement equation.

Nonlinear Dynamic Process Model

Three variables that may be used for the above-mentioned estimation aresensor glucose (SG), calibration factor (CF), and offset. Themeasurement is blood glucose (BG), which, as noted above, is related tosensor current (Isig). Based on the aforementioned variables, thefollowing states may be defined:

-   -   x₁=SG    -   x₂=CF    -   x₃=Offset    -   U=Isig        Using the prior equations relating BG, SG, CF, and the first        order lag, the following is then derived:

$\quad\left\{ \begin{matrix}{{{\overset{.}{x}}_{1}(t)} = {{{- \frac{1}{\tau}}{x_{1}(t)}} + {\frac{1}{\tau}{u(t)}}}} \\{{{\overset{.}{x}}_{2} = {{{x_{2}(t)}t} < T_{d}}};{{\alpha \; {x_{2}(t)}t} \geq T_{d}}} \\{{\overset{.}{x}}_{3} = {x_{3}(t)}}\end{matrix} \right.$

where α=0.995, τ=⅙h=10 min, and u(t)=Isig. As has been noted previouslyin the instant specification and description, sensor response istypically different at the beginning (e.g., first day) of sensor lifethan the remainder of the sensor's life. Therefore, in the instantanalysis, it is also assumed that the sensor response at the beginningis different from the rest of its lifetime. Thus, in the aboverelationship, T_(d) is defined for the first day.

Using the above state variable definitions, the SG measurement, which isan estimation of BG using the finger stick, becomes:

z(t)=x ₂(t)(u(t)+x ₃(t))+v ₁

where z=BG, and u(t) is the first Isig measurement after BG measurement.The sensor glucose is the estimation of blood glucose, i.e.,SG={circumflex over (B)}G. Because the BG measurements are provided insampled form, no discretization is needed in order to implement thediscrete time measurement in the above equation.

In order to apply an Unscented Kalman filter to continuous glucosemonitoring, the above equations for {dot over (x)}(t) and z(t) must bepresented in a nonlinear format, i.e.:

$\quad\left\{ \begin{matrix}{{\overset{.}{x}(t)} = {{f\left( {{x(t)},{u(t)},t} \right)} + {w(t)}}} \\{{z(t)} = {{h\left( {{x(t)},{u(t)},t} \right)} + {v(t)}}}\end{matrix} \right.$

where u is the input, w is the state noise, z is the measurement vector,and v is the measurement noise. It is noted that, while both v and w areassumed to be uncorrelated zero-mean Gaussian white noise sequences,they can be modified depending on statistics that may be captured fromdata. Unlike the Kalman and Extended Kalman filters, the UnscentedKalman filter does not require linearization or discretization of theequations. Rather, it uses a true nonlinear model and approximates thedistribution of the state random variable. Thus, while the goal is stillto compute the Cal Factor, the complexity in the latter computation iscontained within the underlying model and methodology described herein.In other words, within the context of glucose-sensor calibration andoperation, the calibration is performed through the Unscented Kalmanfiltering framework. In this regard, as noted, the (Unscented) Kalmanfilter includes robustness against noise in the calibration by assumingexistence of a noise distribution in both the BG (i.e., the measurementnoise v) and the Isig (i.e., the state noise w), and compensating forsuch noise implicitly in the algorithm. Thus, the unscented Kalmanfilter enables real-time calibration that estimates both Cal Factor andoffset, accounting for changes over time.

Initial Conditions and Covariance Matrix

For the above-described framework, state vector initialization andcovariance are given as:

${\hat{x}(0)} = \begin{bmatrix}{{BG}(0)} \\4 \\{- 4}\end{bmatrix}$ ${P(0)} = \begin{bmatrix}15 & 0 & 0 \\0 & 0.1 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2}$

The diagonal elements of process noise covariance matrix, Q shown below,are variances that represent the uncertainties in the knowledge of eachstate that accumulate between measurements.

$Q = \left\{ \begin{matrix}{{\begin{bmatrix}5 & 0 & 0 \\0 & 0.2 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2}t} < T_{d}} \\{{\begin{bmatrix}5 & 0 & 0 \\0 & 0.1 & 0 \\0 & 0 & 0.1\end{bmatrix}^{2}t} \geq T_{d}}\end{matrix} \right.$

These values should be based upon observations of the unpredictablevariations of these processes when scaled over the measurement time, t.The measurement error variance, R, is equal to 3% of the BG measurementvalue, squared. Thus,

R=0.03×z(t)

With the above structure and methodology, BG measurements are runthrough an Unscented Kalman filter, and the calibration factor isestimated. The calibration factor, in turn, is used to transform Isig toSG, as discussed previously.

FIG. 113 shows a block diagram of an existing calibration process for asingle working electrode. Using the Isig from the working electrode (WEIsig), a pre-processing step 9210 is first performed that may, e.g.,include filtering, averaging, and/or weighting of several Isig valuesfor the single WE to generate a single optimized Isig value. The latteris then calibrated 9220 using the offset and a calibration BG 9230, suchas, e.g., a finger stick meter measurement, to calculate a calibrationfactor CF which, in turn, is used to calculate a sensor glucose valueSG. Post processing 9240 is then performed on the SG to generate a morerobust and reliable sensor glucose value SG.

FIG. 114 shows a block diagram for calibrating a single workingelectrode sensor using a Kalman filter. As before, Isig from the workingelectrode (WE Isig) is the input into a pre-processing step 9212, wherea plurality of Isig values may be, e.g., filtered, averaged, and/orweighted to generate a single optimized Isig value. A calibration BG9232 is then used to calculate a CF and SG in step 9222. However, now,step 9222 is carried out using an unscented Kalman filter, such that thecalculation of the actual calibration factor and the resultant sensorglucose value is carried out through the Kalman filter, using themethodology and relationships described hereinabove. In step 9242, thecalculated SG is subjected to post-processing to generate a more robustand reliable sensor glucose value SG. In an alternative embodiment shownin FIG. 115, the Kalman filter may be used to perform the pre-processingfunctions in addition to the calibration and SG calculation (9217).

Multi-Electrode System and Fusion

In a further embodiment, a Kalman filter may be used to calibrate amulti-electrode system. Specifically, as shown in FIG. 116, a systemwith N working electrodes may have the respective Isig from eachelectrode pre-processed 9214, 9216, 9218, as described hereinabove. Asshown in blocks 9224, 9226, 9228, the processed Isig from each workingelectrode may then be calibrated, and a respective SG calculated, usingan unscented Kalman filter and a calibration BG 9234. The respective SGsfrom each of the N working electrodes may then be fused andpost-processed in block 9244, resulting in a final, fused SG.

It is noted that, while, in the above description, the Kalman filter isapplied in the calibration step only, in alternative embodiments, theKalman filter may be used in one or more of the pre-processing step9214, 9216, 9218, the calibration and SG calculation step 9224, 9226,9228, and/or the SG fusion and/or post-processing step(s) 9244. Inaddition, as shown in FIG. 117, a single Kalman filter can be used tocalibrate all working electrodes together, e.g., by including allelectrodes in the same Kalman filter state space equation. Moreover, thefusion step may be carried out by using the generalized Millman formulaand/or one of the fusion algorithms that were discussed previously inthis specification in connection with fusion of multiple Isig ormultiple SG values (including, e.g., weighting of individual Isig and/orSG values). Thus, the unscented Kalman filter may be used, e.g., inconjunction with EIS data to optimize SG (or Isig) fusion inmultiple-electrode systems.

It is also important to note that, as part of the fusion methodology,the post-processing step which was described previously may include apredictive component, whereby physiological delays between blood glucoseand interstitial glucose may be accounted for. Here, past values ofsensor glucose SG are used to predict a (future) value for SG, with theamount of prediction to be applied at each time step depending on thelevel of noise in the system. FIG. 118 is a table comparing the resultsof applying a current fusion algorithm (“4D Algorithm”), on the onehand, and an unscented Kalman filter, on the other, to various sensordata sets. As shown in FIG. 118, in each instant, application of theKalman filter provided notable improvements in the Mean AbsoluteRelative Difference (MARD) while, at the same, allowing a single Kalmanfilter model to be applied across all of the datasets, even though thereare significant design differences amongst the sensors for which thedatasets were gathered. Thus, e.g., whereas application of the 4DAlgorithm to the Australia dataset resulted in a fusion MARD of 9.72,use of the unscented Kalman filter with the same dataset provided a MARDof 9.66.

As discussed previously in connection with FIGS. 33-35 and 116, fusionalgorithms may be used to generate more reliable sensor glucose values.Specifically, fusion algorithms fuse independent sensor glucose valuesto provide a single, optimal glucose value to the user. Optimalperformance, in turn, may be defined by accuracy, duration and rate ofdata availability, and minimization of fault states that could burdenthe user. As before, it is noted that, while the ensuing discussion maydescribe aspects of a fusion algorithm in terms of a first workingelectrode (WE1) and a second working electrode (WE2) as redundantelectrodes, this is by way of illustration, and not limitation, as thealgorithms and their underlying principles described herein areapplicable to, and may be used in, redundant sensor systems having morethan 2 working electrodes.

In an embodiment of the invention, a SG fusion algorithm is driven by anumber of inputs, such as, e.g., Electrochemical Impedance Spectroscopy(EIS), noise, and calibrations. These inputs dictate how the algorithmcombines independent electrode sensor glucose values to provide thefinal fused sensor glucose value, as well as the logic governingcalibration, data display, and user prompts. Specifically, the fusionalgorithm calculates weights for each individual sensor glucose value(i.e., the glucose value from each of the working electrodes). The sumof the weights must total 1. In other words, the fusion glucose value isa weighted average of the individual sensor glucose values, as definedby the relation:

${FG} = {\sum\limits_{k = 1}^{N}{{SG}_{k} \star {FW}_{k}}}$

where, at a given time, FG is Fusion Glucose, SG_(k) is the sensorglucose value of the k^(th) working electrode, and FW_(k) is the finalfusion weight assigned to the k^(th) SG value for a system with Nworking electrodes.

The weights, to be explored further hereinbelow, are derived viatransformation of a series of fusion inputs, including noise, EIS-basedsensor membrane resistance (Rmem), and calibration factor (Cal Factor,or CF). As has been discussed previously, noise and Rmem are endogenousinputs, driven by the sensor without any explicit input from the user.In this regard, the fusion algorithm will generally favor electrodeswith lower noise and lower membrane resistance. Cal Factor, on the otherhand, is a ratio between the calibration blood glucose values and theraw sensor current value (Isig), and, as such, is derived from userinput. Here, the fusion algorithm will favor electrodes with calibrationfactors that fall within a range defined as optimal. With the “favoredelectrodes” thus defined with respect to noise, Rmem, and Cal Factor,the fusion algorithm then weighs the more-favored electrode(s) moreheavily in the final fused glucose calculation. As shown in FIG. 119,each type of input calculates a set of values that distribute the weightin a ranked fashion, and each type of weight is combined to calculatethe final raw fusion weight.

The fusion inputs are transformed via a series of functions to produce aset of weights. A ratioScore function calculates the raw fusion weightacross a collection of electrodes for a given input (e.g., noise) and,in an embodiment of the invention, may be expressed as:

$r_{k} = {\frac{1}{N - 1}\left( {1 - \frac{\in_{k}}{\sum\limits_{n = 1}^{N} \in_{n}}} \right)}$

This function, or equation, is appropriate for inputs where lower valuesindicate better performance, (e.g., noise and membrane resistance), andtherefore will receive greater fusion weight. Thus, for example, noisefrom all electrodes at a given time is passed to the ratioScorefunction, which assigns to each electrode a score (also referred to asweight or ratio) that is inversely proportional to the amount of itsnoise relative to the sum of noise across all electrodes. In the aboveequation, therefore, the raw noise fusion weight (ratio) at a given time(r_(k)), for working electrode k, is expressed as a function of thenoise on working electrode k (ε_(k)) for a system with N>1 workingelectrodes.

In particular, the first argument in the above ratioScore functionnormalizes the value inside the parentheses so that the sum of r_(k)across all working electrodes totals 1. The second argument inside theparentheses is a ratio of the noise of the individual k^(th) workingelectrode to the sum of noise values across all working electrodes(sigma operator). The ratio is then subtracted from 1 so that anelectrode with low noise receives a high value.

As noted, the above equation applies to inputs for which lower valuesindicate better performance. For inputs where greater values indicatebetter performance, a simpler equation calculates the raw fusion weight.Specifically, the following ratioScore function is used to simplynormalize the given metric δ by the sum across all working electrodes:

$r_{k} = \frac{\delta_{k}}{\sum\limits_{n = 1}^{N}\delta_{n}}$

In the foregoing equation, the input on working electrode k is given byδ_(k) for a system with N>1 working electrodes.

The raw fusion weight scores (or ratios)—as calculated using one of thetwo equations above—are then passed to a ratioGain function, whichemphasizes or deemphasizes the relative scores based on a pre-definedparameter. While raw ratioScore values provide appropriate weighting interms of ranking, they do not necessarily distribute the weights in anoptimal manner. As such, an equation is defined which exaggerates ordeemphasizes the distribution of weight ratios based on a “gain factor”parameter. Thus, in an embodiment of the invention, the gained ratioweight, g, is defined as follows:

$ = {{\frac{1}{N}\left( {1 - m} \right)} + {m \star r}}$

where r is the raw fusion weight ratio, and m is the “gain factor”parameter a for a system with N>1 working electrodes. The output g maythen be saturated to the range [0,1] such that, if the output is greaterthan 1, then the output is set to 1, and if the output is less thanzero, then the output is set to 0. In this regard, a saturation functionthat may be used in conjunction with embodiments of the invention may bedefined as:

${f(x)} = \left\{ \begin{matrix}{a,} & {x < a} \\{x,} & {a \leq x \leq b} \\{b,} & {x > b}\end{matrix} \right.$

It is noted that, in embodiments of the invention, a sigmoidal orotherwise smooth function may also achieve similar results as above.

Finally the values are processed through the makeSumOne function toensure that the sum totals 1, and to normalize if necessary. Thus,individual values divided by the sum of all values yield relativeratios, with the makeSumOne function defined as follows:

$s_{k} = \frac{_{k}}{\sum\limits_{n = 1}^{N}_{n}}$

Diagrammatically, the algorithm discussed hereinabove may be shown fornoise, and Rmem weights, respectively, as follows:

As can be seen from the above diagrams, the calculation of a set ofnoise weights from all individual noise weights follows the same generalalgorithm as that for computing a set of Rmem weights from allindividual Rmem inputs.

In embodiments of the invention, Cal Factor weighting is calculated in asimilar fashion, but with an additional step, involving acalFactorTransform function, as shown below:

Calibration factor values from all electrodes at a given time are firstpassed to the calFactorTransform function. Specifically, the calibrationfactor is transformed to a score via the following function for anormalized log-normal curve:

${f(x)} = {\frac{1}{2\sigma^{2}} \star \frac{e^{{({{{- \ln}\mspace{11mu} x} - \mu})}^{2}}}{x \star e^{({0.5\sigma^{2 - \mu}})}}}$

where x is the raw (input) calibration factor, f(x) is the transformed(output) Cal Factor, and parameters α and μ describe the width and peakof the log-normal curve, respectively.

Next, the results are saturated to the range [0.001, clip], where alltransformed scores greater than the parameter clip will be assignedequal score. Here higher scores will receive greater weight and, assuch, the second of the two ratioScore functions noted above

$\left( {{i.e.},{r_{k} = \frac{\delta_{k}}{\sum\limits_{n = 1}^{N}\delta_{n}}}} \right)$

is used. As shown, the rest of the algorithm follows the proceduredescribed previously for noise and Rmem.

Returning to FIG. 119, the flow diagram of FIG. 119 shows how each setof the weights is combined to calculate the final raw fusion weight.Specifically, the raw Fusion Weight is calculated by weighting andaveraging the noise (9302) and Cal Factor (9304) weights by thenoiseBalance parameter (9308). The combined noise and Cal Factor weightis then weighted and averaged with Rmem weight (9306) by the RmemBalancevariable (9310). For purposes of the forgoing, the parameternoiseBalance (9308) is predefined to specify the balance between noise(9302) and Cal Factor (9304) weights. In a preferred embodiment of theinvention, noiseBalance may be a constant having a value of 0.524.

In addition, the variable RmemBalance (9310) is determined as follows(see also discussion below in connection with FIG. 120): From the time asensor starts, after a pre-defined duration, RmemBalance is set to zero.In other words, after a pre-defined time from sensor start,rawFusionWeight (9318) receives zero contribution from Rmem. Prior tothe pre-defined time—i.e., from the time a sensor starts up until thepre-defined duration—on the other hand, RmemBalance (9310) is calculatedas shown and described below:

First, the min and max Rmem Weights across all electrodes are selected.Then, the min is subtracted from the max, added to 1, and the totaldivided by 2; this operation approximates the variance in weights. Thisvalue is then passed to the TukeyWindow function (described below) whoseoutput is finally subtracted from 1. The purpose of these steps is tocalculate RmemBalance (9310) such that Rmem weight has a greateremphasis on fusion weights when there is a greater variation amongstRmem values.

The TukeyPlus defines a flat-top tapered cosine (Tukey) window where theparameter r defines the ratio of taper over the interval [0,1]. Thenominal tukeyWindow function is described below. Modifications can beimplemented to increase the taper rate by either introducing anadditional “frequency” parameter in front of the a arguments orexponentiating the entire piecewise function:

${f(x)} = \left\{ \begin{matrix}{{\frac{1}{2}\left\lbrack {1 + {\cos \left( {\frac{2\pi}{r}\left\{ {x - \frac{r}{2}} \right\}} \right)}} \right\rbrack},} & {0 \leq x < \frac{r}{2}} \\{1,} & {\frac{r}{2} \leq x < {1 - \frac{r}{2}}} \\{\frac{1}{2}\left\lbrack {1 + {\cos \left( {\frac{2\pi}{r}\left\{ {x - 1 + \frac{r}{2}} \right\}} \right)}} \right\rbrack} & {{1 - \frac{r}{2}} \leq x \leq 1}\end{matrix} \right.$

With the above in mind, a detailed description of the SG fusionalgorithm in accordance with embodiments of the invention will now beprovided. FIG. 120 shows the general outline of the fusion algorithm,which takes as input (9350) respective sensor glucose values (SGs) thathave been calculated for individual sensors (i.e., individual workingelectrodes). It is reiterated that, by way of illustration and notlimitation, FIG. 120 describes the fusion process with reference to twoworking electrodes, each of which generates a respective SG (i.e., SG1and SG2). The algorithm, however, may be applied to a larger number ofworking electrodes.

At block 9352, a determination is made as to whether any of the SGs isinvalid. If both SGs are determined to be invalid (9354), the overallfusion is set to “invalid” (9356). However, if only one of the SGs isinvalid (9358), then the other (valid) SG is set as the Fusion SG (9360,9362). If, on the other hand, all SGs are valid, the next step in theprocess 9370 determines whether the “FUSION_START_TIME_SWITCH” has beenreached. As explained previously in connection with FIG. 119, inembodiments of the invention, this is a pre-defined duration sincesensor start, after which RmemBalance is set to zero. In a preferredembodiment, the pre-defined duration (after sensor connection) afterwhich the fusion algorithm switches from Rmem logic to Cal Factor andNoise logic is about 25 hours.

Thus, if the current time is after the “FUSION_START_TIME_SWITCH”, thenRmem-based fusion is disabled, such that Rmem makes no contribution tothe final fusion weight (9380). If, on the other hand, the current timeis before “FUSION_START_TIME_SWITCH”, then Rmem-based fusion is enabled(9372), such that Rmem fusion weights are calculated as describedhereinabove, and the relative contribution of Rmem fusion weight tofinal fusion weight is calculated based on magnitude of Rmem differences(9374).

Regardless of whether Rmem-based fusion is disabled (9380) or enabled(9372, 9374), the algorithm next provides for calculation of Cal Factorand Noise fusion weights in block 9376. The combined Cal Factor andNoise (CCFN) and Rmem fusion weights are then combined, final fusionweights are calculated and values are smoothed (9377). Finally, as shownin block 9378, SG Fusion is calculated as ri_1*SG1+ri_2*SG2 (for atwo-working-electrode system), where ri_1 and ri_2 are the variablesthat are used to compute fusion weighting.

In connection with the fusion algorithm described herein, the behaviorof each constituent working electrode, which behavior may then beduplicated prior to fusion, may be described as follows in connectionwith a preferred embodiment of the invention:

First Stage Filtering: Conversion of 1 Minute to 5 Minute Values

For each individual working electrode (WE), the algorithm uses the mostrecent 8 minutes of sensor current data to create a five minute Isig.This is referred to as the first stage filtering. The algorithm usesinformation from the system to identify periods in which the sensor datahas been impacted by the diagnostic module. The algorithm then modifiesthe raw sensor signal (1 minute sensor current) by replacing packets inwhich gross noise and/or diagnostic interference is detected.

The algorithm computes (1) discard and (2) five minute Isig byapplication of a simple 7th order FIR filter on the one minute data,using the following coefficients for the filter: [0.0660; 0.2095;0.0847; 0.1398; 0.1398; 0.0847; 0.2095; 0.0660]. The discard flag willbe true or false based on the variability in 1 minute sensor currentmeasurements over the most recent 8 measurements (8 minutes). Thediscard flag will be false when there are fewer than 4 measurementsfollowing a sensor connection. On the other hand, the discard flag willbe true if 4 or more measurements in the buffer fail the followingconditions: (a) 1-minute sensor current is less than 1 nA; (b) 1-minutesensor current is greater than 200 nA; (c) 1-minute sensor current isless than AverageCount±2 with two decimal place precision; (d) 1-minsensor current is greater than AverageCount×2. Here, “AverageCount” isthe average of the middle 4 values if the FIR history has 8measurements; otherwise, it is taken as the average of the existingmeasurements in the FIR history. It is noted that, in a preferredembodiment, the discard-flag-true event will only trigger if the bufferhas 5 or more measurements.

Identification of Invalid Packets

For every 5 minute packet, the signal will be checked to verify if thepacket is valid. If any of the following criteria are met, the packetwill be considered invalid: (a) the 5-minute Isig value is aboveMAX_ISIG or is below MIN_ISIG; (b) the Vcntr is above 0 Volts or lessthan −1.3 Volts: (c) the packet is flagged as an artifact; (d) thepacket was flagged as discard when converting the 1 minute data into the5 minute Isig; (e) 1 kHz Real Impedance is out of range; and (f) Highnoise (see Noise Check section discussed hereinbelow). In a preferredembodiment of the invention, MAX_ISIG and MIN_ISIG, the thresholds usedto identify invalid Isigs, are 200 nA and 6 nA, respectively.

Artifact Detection

On every 5-minute packet, artifact detection may be performed toidentify large and small drops in Isig to prevent the data from beingused in SG calculations. For large drops in Isig, the event may beclassified as a “big artifact”, for which all subsequent packets areflagged as discard and will be considered part of an artifact eventuntil termination conditions are met. Smaller drops, which may beclassified as “small artifacts”, only allow that single packet to beflagged as discard; the following packet can only be flagged as discardby this artifact detection algorithm if it is detected to be a bigartifact. If the packet is flagged as “init” (i.e., initialization, withthe data referring to data during the sensor warm-up period), theartifact detection variables are set to default values and no artifactsare detected.

For every 5-minute packet that is not an initialization packet, twovariables nA_diff_(i) and pct_diff_(i), are defined as follows:

nA_diff_(i) =isig_(i) −isig_(i-1)

pct_diff_(i)=100×(nA_diff_(i) /isig_(i-1))

where isig_(i) represents the value in nA of the ith Isig, andisig_(i-1), is the previous Isig. If the previous packet was not a smallartifact and not a big artifact state, the current packet may be flaggedas a discard if pct_diff_(i)<−25 and nA_diff_(i)<−4.

Identifying Start of Big Artifact

If the previous packet was not a big artifact, the current packet willbe flagged as discard and considered the start of a big artifact if anyof the 3 conditions below are true:

pct_diff_(i)<−40 AND nA_diff_(i)<−5

pct_diff_(i) +pct_diff_(i-1)<−50 AND nA_diff_(i)+nA_diff_(i-1)<−13

pct_diff_(i) +pct_diff_(i-1) +pct_diff_(i-2)<−60 ANDnA_diff_(i)+nA_diff_(i-1)+nA_diff_(i-2)<−18

After Detection of a Big Artifact

For every packet in the big artifact state, including the packetdetecting the artifact, the packet flagged as discard. Once detected asan artifact, the state of an artifact is determined on each packet. Inthis regard, valid states are: (1) Falling; (2) Nadir Stability; and (3)Rising. Exit from the big artifact state can occur if any of thefollowing 4 conditions is met: (1) Isig is high and stable after beingin the Rising State; (2) Previous state was Rising, Isig is stable, andsystem has been in the Rising state for several packets; (3) The systemhas been in the artifact state for a prolonged period, the maximumlength being defined upon detection of the artifact; and (4) There is adisconnect.

Small Dropout Detection

The dropout structure is updated every packet and indicates if thecurrent packet is in a dropout, and has associated variables so thefilter can account for the dropout. The overall logic is as follows: Adropout state is detected as any of the following three generalconditions: (1) A rapid drop: A rapidly decreasing Isig, while previouspackets showed a more stable signal; (2) A directional change: Amoderately fast decreasing Isig with previous packets having low noiseand an increasing Isig; (3) A moderate drop: Isig decreasing at amoderate level with previous packets showing very low noise. Once any ofthese events is detected, the measured decrease in Isig is added back tothe raw Isig prior to filtering, and the Isig threshold to exit thedropout state is defined. The logic exits from the dropout state if thisstate persists for too long or the Isig increases sufficiently.

Noise Estimate

Next, noise_level and freq_equiv are determined for the current packet,which are then used in the filtering section. The noise_level isadditionally used in identifying dropouts and identifying a sensor endcondition (see section on NoiseCheck). This process requires the twomost-recent values for noise_level. Specifically, noise_level iscalculated based on the absolute value of the seven (7) most-recentsecond derivative of Isig (isig_acc) values, scaled by 9× calFactor, andclipped to be between 0 to 10. In a preferred embodiment, a defaultnoise_level may be set of 7.5 if the current or prior second derivativecalculation was not performed. The variable freq_equiv is calculated asfollows, using the five (5) most-recent unfiltered Isig rate of changevalues:

Freq_equiv=abs(mean(roc))*calFactor

where “roc” is the rate of change in nA/min. After the abovecalculation, the freq_equiv value is then clipped to 0.2 to 4 mg/dL/min.If three or more isig_acc values are invalid, or the noise_levelcalculated is over 7, then freq_equiv is set to a default value of 0.9.

Rates of Change (ROC) Estimate

The first and second derivatives of Isig are used to estimate noise,identify dropouts in the signal, compensate for delay, and reduce thefalse errors when performing the instant calibration error check. Bothfiltered and unfiltered rates of change are calculated. In connectionwith the former, a Savitzky-Golay smoothed rate of change is calculatedusing the 5 most-recent Isig values, and replacing any invalid Isigswith the most-recent valid Isig. Thus:

Weights=[0.2; 0.1; 0; −0.1; −0.2]; % same as coeff/Norm: [2; 1; 0; −1;−2]/10

roc_savitisig=sum(rawisig.*weights)/time_since_last_packet;% unitsnA/min

The unfiltered Isig rate of change (variable roc_rawisig) is calculatedby subtracting the prior Isig from the current Isig, and dividing by thetime difference (5 minutes). The second derivative of the unfilteredIsig (acc_rawisig) is calculated by subtracting the (first derivative)roc_rawisig value calculated with the prior packet from the currentpacket and dividing by the time difference, as follows:

acc_rawisig=(roc_rawisig(1)−roc_rawisig(2))/5

Isig Filtering

The calculations that are used to determine fIsig, the filtered Isigvalue used for calibration and calculating SG, will now be described.The filter parameter “q” adapts based on the noise_level and freq_equiv,so that under low noise or high rates of change, fIsig will be close tothe unfiltered value. When Isig data is invalid, the filter outputremains unchanged from the previous output. The filter will be reset atSENSOR_WARMUP_TIME, which is defined as the time after sensor connectionwhen SGs may begin to be displayed to the user. In preferred embodiment,SENSOR_WARMUP_TIME is about one hour.

If the resulting fIsig is an unexpected value, specifically above 202.5nA or under 3.5 nA, a Change Sensor alert is issued. If the resultingfIsig is greater than or equal to 3.5 nA and less than MIN_ISIG, then itwill be clipped at MIN_ISIG. As noted previously, in preferredembodiments of the invention, MIN_ISIG may be set at 6 nA. However, ifthe resulting fIsig is less than or equal to 202.5 nA and greater thanMAX_ISIG, then it will be clipped at MAX_ISIG. As has been describedpreviously, in preferred embodiments of the invention, MAX_ISIG may beset at 200 nA.

Isig Delay Compensation

Employing a Kalman filter, a predicted Isig is used as the measurementinput. The prediction, in turn, is calculated based on the Isig rate ofchange, clipped to prevent adding excessive prediction. The amount ofprediction added is regulated by the presence of invalid data and noise(from noise_level) calculation.

Kalman_State Calculations

The kalman_state.q value (used in the ensuing equations) is calculatedusing the noise_level and freq_equiv values described in the NoiseEstimate section. If the system is in a dropout, roc is not added toIsig. Instead, the dropout amount is added, and the kalman_state.qcalculated is modified to provide more filtering. The followingcalculations are used to determine the values to store forkalman_state.x and kalman_state.p. The value for cur_isig includes thedelay compensation added to the five minute Isig.

Kalman_state.p=kalman_state.p+kalman_state.q

kalman_state.k=kalman_state.p/(kalman_state.p+kalman_state.r)

kalman_state.x=kalman_state.x+kalman_state.k*(cur_isig−kalman_state.x)

kalman_state.p=(1−kalman_state.k)*kalman_state.p

EIS Events

Every time an EIS event is triggered, measurements are taken on thefollowing frequencies (in Hz), with the sequence being repeated per WE:[0.105, 0.172, 0.25, 0.4, 0.667, 1, 1.6, 2.5, 4, 6.3, 10, 16, 25, 40,64, 128, 256, 512, 1024, 2048, 4096, 8192]. If one of the EISmeasurements is flagged as saturated or discard, the entire set ofmeasurements per WE will not be used.

Blood Glucose (BG) Entry

As has been noted, the calibration ratio (CR), which is used for thecalibration error checks, may be calculated as follows:

cr=bg/(fisig+offset)

Only BG entries greater than or equal to 40 mg/dL and less than or equalto 400 mg/dL are used for calibration, and values outside this rangewill be rejected. If no new sensor command or old sensor command hasbeen received, or the most recent packet was flagged as “init”, the BGwill be rejected. If no packet exists prior to the BG entry (such asafter a new sensor command), the BG entry will be rejected. The BG entrywill be rejected if the timestamp indicates it is too old or in thefuture.

Instant Calibration Error Check

If a BG is not rejected by the basic checks, it will be checked for acalibration error using the most recent fIsig from both WEs value. In apreferred embodiment of the invention, this is the only place where acalibration error will be issued. If there is a calibration error onboth WEs, a new, successful BG entry will be required to continueshowing SG value, and the BG which caused the calibration error will notbe used for calibration. The following conditions are considered singleWE calibration errors: (a) The previous packet has an invalid Isig; (b)The CR is outside the calibration error thresholds; (c) The CR isdifferent, e.g., beyond a threshold, from both the previous CR and thecurrent calFactor; (d) Larger thresholds are used if the system expectshigher error, specifically in the FDC adjustment, IsigDip adjustmentmode, or the estimated rate of change exceeds 1.5 mg/dL/min. Inpreferred embodiments of the invention, calibration error thresholds maybe set as follows: 40 mg/dL for a smaller threshold used for typical CEchecks (THRESH_MGDL), and 50 mg/dL for a larger threshold(THRESH_MGDL_LARGE), used when larger errors are expected during CEchecks.

When a BG entry does not cause a calibration error, the single WEcalibration error counter will be set to 0, and the BG will be used toupdate the calFactor. If the algorithm identifies a BG as causing asingle WE calibration error, but a BG is pending final calibration, theBG is rejected, and calibration continues, using the previously acceptedBG on that WE. If a new BG passes the calibration error checks, itreplaces any current BG values that are pending final calibration. Ifthe algorithm identifies a BG as causing a calibration error not due toan invalid Isig, and the above does not apply, then: (1) if thecalibration error counter is 1, and less than 5 minutes have elapsedsince the transmitter identified the previous calibration error, the BGwithout incrementing the calibration error counter, thereby preventing achange sensor alarm from occurring from the same BG and fisig whichpreviously caused a calibration error; and (2) otherwise, thecalibration error counter is increased. If the counter was 0, then a newBG error is required to continue showing SG. Once the calibration errorcounter reaches 2 on a single WE, the WE is terminated, as SG can nolonger be calculated.

Embodiments of the invention include a dynamic maximum CR limit.Specifically, the MAX_CR may be set at 16 at sensor startup, and reducedlinearly, as a function of time, to 12 over 4 days. The MAX_CR may befurther gradually reduced to 10 if the Vcntr value is high for aprolonged time. As has been described previously, a high Vcntr value istypically associated with high levels of noise in the Isig, as well assensitivity loss.

Working Electrode Calibration

As has been described herein, individual working electrodes willrequest/require calibration according to fixed intervals, or asdetermined in real-time by Smart Calibrations. In this regard, in anembodiment of the invention, the first successful calibration may expirein 6 hours, with subsequent calibrations expiring in 12 hours. SmartCalibrations, based on EIS or First Day Calibration logic, may result inthe expiration time being shorter, as discussed in the First DayCalibration and EIS sections.

In a preferred embodiment, the algorithm will continue to calculate SGfor an additional amount of time after standard calibration expiration(EXTRA_TIME), as well as after EIS Smart Calibration expiration(EXTRA_TIME_SMART). Accordingly, work electrode state is set to 1 ifcalFactor is expired, but within EXTRA_TIME or EXTRA_TIME_SMART, and setto 2 if calFactor is expired and after EXTRA_TIME or EXTRA_TIME_SMART.These SGs are stored in a separate SG buffer that does not affect thedisplay of SG. In embodiments of the invention, EXTRA_TIME is set to 12hours, and EXTRA_TIME_SMART is set to 6 hours.

Individual WE SG Calculation

The Cal Factor used to calculate SG is based on the most recentcalibration calculation or, if in an adjustment mode, the value updatedthrough the First Day Calibration Logic or Isig Dip Calibration Logic.The Cal Factor used to calculate SG must be less than MAX_CR and greaterthan MIN_CR. If the Cal Factor is outside of this range, the system willinvalidate the Cal Factor and set the working electrode state equal to2. Similarly, the filtered Isig used to calculate SG must be less thanMAX_ISIG and greater than MIN_ISIG. If the filtered Isig is outside ofthis range, the system will invalidate the Isig and set the workingelectrode state equal to 2. Working electrode state is set to 2 if CalFactor is expired or invalid, or the current packet is invalid.

BG to Isig Pairing

After a BG entry that did not cause a calibration error, the followingsteps are performed to update the Cal Factor. If the current packet isinvalid or the new BG would cause a calibration error, the Cal Factor isnot updated at this time. If the current packet is valid and the BGwould not cause a calibration error, a temporary update of thecalibration buffer is performed by adding the BG and current pairedsensor information to the calibration buffer and temporarily removingthe oldest paired information. The Cal Factor is then calculated asdescribed in the Cal Factor calculation section hereinbelow. If thereare previous calibrations, the calculated Cal Factor value must beweighted with respect to the previous Cal Factor. In a preferredembodiment, the weight is assigned as follows: 70% weight for new value,and 30% weight on old value. It is noted that, for a packet which occurs5 to 10 minutes after a successful BG entry, the calibration factor isupdated by selecting the most recent fIsig value which is closest to theprior calibration factor and does not cause a violation of thecalibration error criteria.

Calibration Buffer Update

In embodiments of the invention, the calibration buffer contains BGvalues, as well as the following paired information: the paired Isigvalue associated with each BG value in the buffer, the higher-frequencyimaginary impedance expected value, and the range expected impedancevalue. There are generally 4 positions in the calibration buffer, withposition 4 being the oldest entry. If the system is in Isig Dip Mode,and the CR is less than the most recent CR in the calibration buffer,then the calibration buffer is updated by replacing the most recententry (position 1) in the calibration buffer with the pending entryinstead of removing the oldest entry. If, however, the latter does notapply, the calibration buffer is updated by shifting the prior entries(removing the oldest entry at position 4), and putting the new pendingBG at position 1.

Cal Factor Calculation

If there is no calibration error, the Cal Factor may be updated inaccordance with the following relation, where Isig is the paired Isigvalue, and n is the number of valid entries in the calibration buffer:

${{Cal}\mspace{14mu} {Factor}} = \frac{\sum\limits_{i = 1}^{n}{\alpha_{i} \times \beta_{i} \times \left( {{isig}_{i} + {offset}} \right) \times {BG}_{i}}}{\sum\limits_{i = 1}^{n}{\alpha_{i} \times \beta_{i} \times \left( {{isig}_{i} + {offset}} \right)^{2}}}$

In addition, in a preferred embodiment, Alpha weights are fixed for eachBG entry in the calibration buffer such that the most recent BG entry(i.e., position 1) has a weight of 0.80, position 2 has a weight of0.13, position 3 has a weight of 0.05, and position 4 has a weight of0.02. In the preferred embodiment, Beta weights for each BG entry arecalculated using the equation as follows, with i indicating the positionin the calibration buffer:

beta(i)=2.655×(BG(i)−0.8041)−0.01812

The Cal Factor calculated is weighted with the expected_cf_value if thesystem is not in FDC mode and EIS has not detected a sensitivity change.The expected_cf_value carries a 20% weight and the calculated Cal Factorhas an 80% weight. The Expected Cal Factor is calculated as follows:

expected_cf_value=0.109*t+4.731

where t=days from sensor start. If the system is in the Isig DipCalibration mode, and the calculated Cal Factor is less than 75% of theCR, the Cal Factor is set to 75% of the CR. This ensures that the BG andSG values are reasonably close following a calibration during an IsigDip.

Individual WE SG Calculation

Sensor glucose values are calculated in accordance with the relation

SG=(fisig+offset)×calFactor+predictedSGchange

where The predictedSGchange value is a 5-minute predicted value that iscalculated based on the filtered Isig, and moderated based on signalnoise and glucose concentration. If the predictedSGchange is more than 6mg/dL or less than −6 mg/dL, it will be clipped at 6 mg/dL or −6 mg/dL,respectively. In addition, the calculated SG is rounded to two decimalplaces.

First Day Calibration Mode

As described previously, the First Day Calibration adjustment, referredto as FDC, addresses situations when the initial calibration factorindicates there is an abnormal calibration factor. While in FDC, thealgorithm will adjust the Cal Factor towards a target range. For entryinto FDC mode, if the first successful BG entry indicates thecalibration ratio is outside the normal range of 4.5 to 5.5 mg/dL/nA,but inside the calibration error thresholds, then the FDC mode for thatWE will be turned on. In this mode, the Cal Factor will be calculatedusing the most recent BG and fisig, and then adjusted as set forthbelow.

When the First Day Calibration mode is active, the Cal Factor for thatWE will be adjusted on each 5 minute packet in accordance with:

cfAdjust=(p1×origCF+p2)×5/60

calFactor=calFactor+cfAdjust

where P1=−0.1721 hour−1, and p2=0.8432 mg/dL/nA/hour. First DayCalibration adjustment will not take place for the current packet ifeither: (1) cfAdjust is negative and the SG is already low (under 75mg/dL); or (2) the adjusted Cal Factor has reached target range (4.5 to5.5 mg/dL/nA).

FDC mode per WE will stop and no additional adjustment allowed for thesensor when 12 hours have passed since the start of the sensor, or a newcalibration entry has a CR within the stable range (4.5 to 5.5mg/dL/nA). While the system is in FDC mode, the calibration expirationtime is 6 hours. However, in connection with Smart Calibrations, if theinitial accepted calibration has a CR outside a wide range (under 4mg/dL/nA or above 7 mg/dL/nA) for both WEs, the first calibration willexpire in 3 hours.

Isig Dip Calibration Mode

Embodiments of the invention use Isig Dip Calibration logic in responseto certain calibrations which are suspected to occur on Isigs that arelow for the glucose concentration. The logic returns the Cal Factorcloser to the prior value. Isig Dip Calibration mode is turned on if theWE is not in the FDC mode and, at calibration, the calibration indicatesthat the Isig is low, and a prior calibration was successful. This isverified by comparing the following thresholds:

-   -   CR>1.4×previous calFactor (termed origCF)    -   Previous calFactor<6 mg/dL/nA    -   Average value of recent valid Isigs<20 nA        The fIsig value used to calculate the Cal Factor on the Isig Dip        is subsequently used in an adjustment logic as described below,        and will be termed triggerIsig. In addition, the previous Cal        Factor is used to determine if the Isig Dip Calibration mode        should exit. This previous Cal Factor is termed origCF.

If Isig Dip Calibration mode is on, Isig is monitored for recovery. Inan embodiment of the invention, recovery is detected when the currentfIsig value is more than 1.4× triggerIsig. Once a recovery is detected,the Cal Factor will be adjusted as long as the fIsig is abovetriggerIsig. The Cal Factor is adjusted at a rate which would return theCal Factor to the origCF value in 12 hours.

Isig Dip Exit

The algorithm will stop adjustment and exit the Isig Dip Calibrationmode if any of the following are true, where Cal Factor is the mostrecent (possibly adjusted) Cal Factor:

-   -   calFactor<origCF×1.2    -   calFactor<5.5    -   More than one day has passed since the detection of the Isig        Dip.    -   A new BG at calibration time shows CR<1.25×origCF.

EIS Smart Calibrations

At every EIS measurement, a 5 point moving average filter is used tofilter the 1 kHz imaginary impedance. If it has been less than one hoursince the previous calibration, the expected 1 kHz imaginary impedancevalue of the previous calibration is set to the current filtered value,and the allowed range for the 1 kHz imaginary impedance value is setbased on recent EIS measurements. If it has been over one hour since theprevious calibration, and the current filtered impedance value isoutside the allowed range for both WEs, the calibration expiration timeis reduced to a maximum of six hours from the previous calibration. Ifcalibration is taking place when sensitivity change has been detected,then, if the CR is >15% different than the most recent CR in thecalibration buffer, only the new and previous BG are kept in thecalibration buffer, the expected_cf_value is not used to calculate theCF.

Working Electrode State

Each individual working electrode is assigned a state that determineshow information from that electrode is used for subsequent processing.The states are determined by various error checks, diagnostics, andcalibration statuses. The following table summarizes the states:

Description State Conditions Normal 0 Normal Intermediate 1 CalibrationRecommended Invalid 2 Discard; Invalid; Artifact Noise EIS Vcntr CalError Calibration Required

Noise

If two consecutive windows occur with high noise (per abovecalculation), the Isig data will be considered invalid (state=2) untilthe end of the two hour window (at which point the work electrode mayeither be terminated or this logic will no longer flag the data asinvalid). If three consecutive two hour windows occur with high noise(per above calculation), the work electrode state is set to 2irreversibly and is considered terminated.

EIS—Working Electrode Termination Based on 8 kHz Imaginary Impedance

At every EIS measurement, a 5 point moving average filter is used tofilter the 8 kHz imaginary impedance. The filtered value is monitoredfor 36 hours from sensor connection. After 36 hours, the minimum 8 kHzfiltered imaginary impedance value is set as the reference, excludingthe values taken during the warmup period. In a preferred embodiment ofthe invention, the latter reference value is clipped to the range:−1,000Ω to 800Ω. Once the reference is set, the absolute differencebetween the filtered 8 kHz imaginary impedance value and the referencevalue id calculated at every EIS measurement. The working electrodestate is set to 2 irreversibly and terminated if the difference islarger than 1,200Ω for two consecutive packets.

EIS—WE Termination and Error Based on 1 kHz Real Impedance

At every EIS measurement, a 5 point moving average filter is used tofilter the 1 kHz real impedance. The filtered real impedance value ismonitored until the filtered and unfiltered values are below 7,000Ω. Ifthe unfiltered 1 kHz real impedance value is above 10,000Ω, an error istriggered and the state is set to 2. If the condition persists for 3hours, the working electrode is terminated. If the filtered 1 kHz realimpedance is above 12,000Ω, the state is set to 2, and the workingelectrode is terminated.

Fusion

As described hereinabove in connection with FIG. 120, in a preferredembodiment of the invention, the fusion algorithm proceeds as follows:If both WE SGs are invalid or in state 2, then fusion SG is set asinvalid. If only one WE SG is invalid or in state 2, then fusion SG isequal to the other valid WE SG. The fusion algorithm includes two modesof weight calculation, and logic describing how to transition betweenthe two modes.

RMEM Fusion Mode

Rmem Fusion leverages the differences in Rmem on each working electrodeto determine fusion weighting. In General, the working electrode withthe lower Rmem will receive the greater fusion weight. In this regard,Rmem from each working electrode's EIS measurement is calculated priorto the latest successful calibration, and the values are stored.

Combined Cal Factor and Noise (CCFN) Fusion Mode

Combined Cal Factor and Noise Fusion mode use these two metrics todetermine fusion weight. Cal Factor Fusion leverages the Cal Factor oneach working electrode to determine fusion weighting. The Cal Factor oneach working electrode is transformed via a lookup table or functionwhereby CFs that are within a pre-defined range receive greater weight.Thus, to calculate the Cal Factor Weight (cfWeight1) metric, the CalFactor is transformed, as described hereinabove, such that extremevalues receive a weight of zero, optimal values receive a weight of one,and intermediate values receive weights between zero and one. Thetransform function is a normalized log-normal curve which is, as notedpreviously, defined by the parameters (Fusion) μ, which describes theCal Factor transform log-normal curve peak, and (Fusion) σ, whichdescribes the Cal Factor transform log-normal curve width. In preferredembodiments, μ may have a value of 1.643, and σ may have a value of0.13.

The output of the log-normal transform is saturated to [0.001,FUSION_CLIP], where the lower saturation limit is to prevent divide byzero errors downstream, and the upper saturation limit equalizes allscores above the parameter FUSION_CLIP. In a preferred embodiment,FUSION_CLIP may be set to 0.6. Finally, the transformed, saturated CalFactor for each working electrode is normalized by the sum across theworking electrodes, and the ratio is passed through the ratioGainfunction.

Noise-Based Fusion

Noise Fusion leverages the differences in noise on each workingelectrode to determine fusion weighting. In general, the workingelectrode with the lesser noise will receive the greater weight. Thefiltered noise from each working electrode is calculated via a movingaverage filter of length FUSION_NOISEWINDOW on the absolute value of thevariable containing the second derivative of the raw Isig (acc_rawisig)from each working electrode. In a preferred embodiment,FUSION_NOISEWINDOW is set to 36 hours. It is noted that, prior to theavailability of FUSION_NOISEWINDOW number of packets (e.g., duringwarmup), the moving average filter length is equal to the number ofavailable packets.

Next, in order to avoid dividing by zero, each WE's filtered noise valueis saturated such that if filteredNoise<0.001, then filteredNoise=0.001.Then, a Noise Weight Metric is assigned to each WE by using the otherWE's saturated filteredNoise value, normalized by total noise. Asdescribed in detail hereinabove, in this way, the WE with the lowernoise receives a greater weight. Finally, the Cal Factor and Noisemetrics are combined as set forth above in connection with FIG. 119.

Fusion Mode Transition

Different modes of Fusion may be appropriate for the sensor depending onthe sensor's status. The Rmem fusion mode is generally most appropriateearlier in the sensor wear. The Cal Factor and Noise fusion is mostappropriate later in wear. In order to transition between these modes offusion, in a preferred embodiment of the invention, afterFUSION_START_TIME_SWITCH, fusion weighting is completely determined byCCFN. This Time Scheduled Switching logic supersedes Rmem SimilarityTransitioning.

Rmem Similarity Transitioning

The logic for transitioning fusion mode depends on the similaritybetween the WE Rmem values. A large difference in Rmem means the finalfusion value is to be dominated by Rmem based fusion. As the differencein Rmem values approaches zero, Rmem fusion weights approach 0.5. Atthis point, it is appropriate for Combined Cal Factor and Noise Fusion(CCFN) to have a greater influence on final fusion weights. Fusionweight values are calculated as shown, e.g., in FIG. 119.

Fusion Weight Smoothing

A symmetric weighted moving average is applied to the fusion weightvalues after being computed. This avoids sharp transitions in caseswhere sharp transitions occur due to one of the working electrodesbecoming unreliable. Sharp transitions are allowed at calibration. Forthis purpose, the coefficients of the filter are: [1 2 3 4 4 3 2 1]/20.

Fusion SG Calculation and Display

When fusion is enabled, the fused SG value is the final weighted sum ofthe plurality of working electrode SGs. Thus, for a system with 2working electrodes:

filteredRi_2(t)=1−filteredRi_1(t)

fused_sg(t)=(filteredRi_1(t)×cur_sg(1)+filteredRi_2(t)×cur_sg(2))

where filteredRi_1(t) is the filtered fusion weight for WE1, and thefused SG value is rounded to 0 decimal places. It is noted that, in apreferred embodiment, the displayed fusion SG must be within the range[40, 400]. If the calculated fusion SG is below 40 mg/dl, the displaywill show “<40 mg/dl”, and if the calculated fusion SG is above 400mg/dl, the display will show “>400 mg/dl”.

Fusion Rate of Change (ROC) Calculation

The SG rate of change may be calculated on every 5 minute packet. Here,roc1 and roc2 are first calculated as follows, using the three mostrecent fusion SG values, where fused_sg(1) is the most recent fusion SGvalue:

roc1=(fused_sg(1)−fused_sg(2))/5

roc2=(fused_sg(2)−fused_sg(3))/5

If the direction (sign) of roc1 is different from roc2, or any of themost 3 recent SGs is blanked for SG display, the SG rate of change isset to zero mg/dL/min. Otherwise, the fused_sg rate of change is thevalue of roc1 or roc2 that is closer to zero.

Calibration BG Request and Coordination

Individual WEs can trigger calibration BG requests. However, the userwill be prompted for calibration BG requests only when all functioningWEs have calibration requests outstanding. An exception to the foregoingis the first calibration request, which is to occur at or afterSENSOR_WARMUP_TIME, as discussed previously. Here, the user will beprompted for the first calibration BG request when any functioning WEhas calibration requests outstanding.

Calibration may be displayed to the user as either “recommended”, or“mandatory”. “Calibration recommend” logic is triggered according to thecalibration schedule (i.e., 2 calibrations per day plus smart cals, in apreferred embodiment). As noted, EXTRA_TIME is allowed to lapse beforecalibration becomes mandatory and SG computation stops. This time is setto EXTRA_TIME_SMART when a calibration is caused by a smart cal. Basedon when a smart cal is triggered relative to the last successfulcalibration, data may continue to be displayed for 6-12 hours. The stateof the SG is recorded so that the display device may determine if or howto display the SG during “calibration recommended” states. The tablebelow is a graphical representation of the logic:

WE1 WE2 Fusion Calibration Calibration Calibration State State StateNone None None None Recommended None None Mandatory None Recommended*Recommended* Recommended* Recommended* Mandatory Recommended* MandatoryMandatory MandatoryIt is noted that the states in table above are summarized for brevity.Thus, the complete logic table can be generated by switching WE1 andWE2. In addition, the user is exposed only to the “fusion calibration”state.

While the description above refers to particular embodiments of thepresent invention, it will be understood that many modifications may bemade without departing from the spirit thereof. Additional steps andchanges to the order of the algorithms can be made while stillperforming the key teachings of the present invention. Thus, theaccompanying claims are intended to cover such modifications as wouldfall within the true scope and spirit of the present invention. Thepresently disclosed embodiments are, therefore, to be considered in allrespects as illustrative and not restrictive, the scope of the inventionbeing indicated by the appended claims rather than the foregoingdescription. All changes that come within the meaning of, and range of,equivalency of the claims are intended to be embraced therein.

What is claimed is:
 1. A method of calculating a single, fused sensorglucose value based on respective sensor glucose values of a pluralityof redundant working electrodes of a glucose sensor, comprising:performing respective electrochemical impedance spectroscopy (EIS)procedures for each of the plurality of redundant working electrodes toobtain values of membrane resistance (Rmem) for each said workingelectrode; calculating a respective Rmem fusion weight for each saidworking electrode based on the respective Rmem value for each of theplurality of working electrodes; measuring a noise value for each of theplurality of working electrodes; calculating a respective noise fusionweight for each said working electrode based on the respective noisevalue for each of the plurality of working electrodes; measuring acalibration factor (CF) value for each of the plurality of workingelectrodes; calculating a respective CF fusion weight for each saidworking electrode based on the respective CF value for each of theplurality of working electrodes; for each of the plurality ofelectrodes, calculating an overall fusion weight based on saidelectrode's Rmem fusion weight, noise fusion weight, and CF fusionweight; and calculating said single, fused sensor glucose value based onthe respective overall fusion weight and sensor glucose value of each ofthe plurality of redundant working electrodes.
 2. The method of claim 1,further including performing a validity check on said respective sensorglucose values.
 3. The method of claim 2, wherein the fused sensorglucose value is determined to be invalid if all of the sensor glucosevalues are invalid.
 4. The method of claim 2, wherein the glucose sensorincludes two redundant working electrodes, and wherein, if the sensorglucose value for one of said two working electrodes is valid and thesensor glucose value for the other of the two working electrodes isinvalid, then the fused sensor glucose value is equal to the validsensor glucose value.
 5. The method of claim 1, wherein said Rmem valuesare obtained based on respective values of 1 kHz real impedance.
 6. Themethod of claim 1, further including, for each working electrode,combining the respective noise fusion weight and CF fusion weight tocalculate a combined noise and CF fusion weight.
 7. The method of claim6, wherein said combined noise and CF fusion weight is calculated byweighting and averaging the respective noise fusion weight and CF fusionweight by a predefined parameter.
 8. The method of claim 1, wherein,after a predefined period of time from sensor start, the value of Rmemfusion weight is equal to
 0. 9. The method of claim 8, wherein saidpredefined period of time is about 25 hours.
 10. The method of claim 8,wherein, between sensor start and expiry of said calculated period oftime, the value of Rmem fusion weight is modified by a first variable togenerate a modified Rmem fusion weight, said variable being a functionof the variance in respective Rmem fusion weight values for theplurality of working electrodes.
 11. The method of claim 10, furtherincluding, for each working electrode, combining the respective noisefusion weight and CF fusion weight to calculate a combined noise and CFfusion weight.
 12. The method of claim 11, wherein said combined noiseand CF fusion weight is calculated by weighting and averaging therespective noise fusion weight and CF fusion weight by a predefinedparameter.
 13. The method of claim 12, further including modifying saidcombined noise and CF fusion weight by a second variable to calculate amodified combined noise and CF fusion weight.
 14. The method of claim13, wherein said overall fusion weight is calculated based on saidmodified Rmem fusion weight and said modified combined noise and CFfusion weight.
 15. The method of claim 13, wherein the sum of the valuesof said first and second variables equals
 1. 16. The method of claim 1,wherein each said respective EIS procedure is performed for a range offrequencies.
 17. A program code storage device comprising: acomputer-readable medium; and computer-readable program code, stored onthe computer-readable medium, the computer-readable program code havinginstructions which, when executed, cause a physical microcontroller toperform a method of calculating a single, fused sensor glucose valuebased on respective sensor glucose values of a plurality of redundantworking electrodes of a glucose sensor by: performing respectiveelectrochemical impedance spectroscopy (EIS) procedures for each of theplurality of redundant working electrodes to obtain values of membraneresistance (Rmem) for each said working electrode; calculating arespective Rmem fusion weight for each said working electrode based onthe respective Rmem value for each of the plurality of workingelectrodes; obtaining a noise value for each of the plurality of workingelectrodes; calculating a respective noise fusion weight for each saidworking electrode based on the respective noise value for each of theplurality of working electrodes; obtaining a calibration factor (CF)value for each of the plurality of working electrodes; calculating arespective CF fusion weight for each said working electrode based on therespective CF value for each of the plurality of working electrodes; foreach of the plurality of electrodes, calculating an overall fusionweight based on said electrode's Rmem fusion weight, noise fusionweight, and CF fusion weight; and calculating said single, fused sensorglucose value based on the respective overall fusion weight and sensorglucose value of each of the plurality of redundant working electrodes.18. The device of claim 17, wherein the computer-readable program codehas instructions which, when executed, further cause the microcontrollerto perform a validity check on said respective sensor glucose values.19. The device of claim 17, wherein the computer-readable program codehas instructions which, when executed, further cause the microcontrollerto, for each working electrode, combine the respective noise fusionweight and CF fusion weight to calculate a combined noise and CF fusionweight by weighting and averaging the respective noise fusion weight andCF fusion weight by a predefined parameter.
 20. The device of claim 19,wherein the computer-readable program code has instructions which, whenexecuted, further cause the microcontroller to, for each workingelectrode, modify the value of Rmem fusion weight by a first variable togenerate a modified Rmem fusion weight, said variable being a functionof the variance in respective Rmem fusion weight values for theplurality of working electrodes.
 21. The device of claim 20, wherein thecomputer-readable program code has instructions which, when executed,further cause the microcontroller to modify said combined noise and CFfusion weight by a second variable to calculate a modified combinednoise and CF fusion weight.
 22. The device of claim 21, wherein thecomputer-readable program code has instructions which, when executed,further cause the microcontroller to calculate said overall fusionweight based on said modified Rmem fusion weight and said modifiedcombined noise and CF fusion weight.